Federico Cafiero (24 May 1914 – 7 May 1980) was an Italian mathematician known for his contributions inreal analysis,measure andintegration theory, and in the theory ofordinary differential equations. In particular, generalizing theVitali convergence theorem, theFichera convergence theorem and previous results ofVladimir Mikhailovich Dubrovskii, he proved a necessary and sufficient condition for the passage to thelimit under the sign ofintegral:[3] this result is, in some sense, definitive.[4] In the field of ordinary differential equations, he studied existence and uniqueness problems under very general hypotheses for the left member of the given first-order equation, developing an important approximation method and proving a fundamental uniqueness theorem.[5]
He was appointed instructor of the course of "Elementi di matematica"[10] by the Faculty of Statistical Sciences of the University of Rome, for the 1940–1941 academic year:[11] however, he was able to hold the course only for a few months, since he was called to arms in January 1941[12] and stationed from May 1942 to September 1943 on the Northern African coasts as anofficer of theSan Marco Battalion.[13] It was there that, after having successfully completed a dangeroussabotage operation, theArmistice between Italy and Allied armed forces surprised him and the other members of his unit, leaving them without any support.[12] Nonetheless, in desperate conditions, he was able to lead his men to theItalian coasts with arubberdinghy, and was awarded aSilver Medal of Military Valor for this act.[12]
Rebuilding and researching: the years from 1944 to 1953
Being discharged fromMilitary Service in February 1944,[7] he was not able to reach Rome and remained in Napoli.[12] The institution which currently is the Institute of Mathematics of the University of Naples was on the way of reconstituting,[14] the eight former mathematics institutes of the university having been literally "torn to pieces" by theAllied forcesMilitary Police.[15] It was necessary to collect and reorder in a new library all the volumes of the previously existed ones, then piled on the floor of a single room, catalogue themex novo and create new records, provide the library administration, and of course there was no administrative personnel available nor financial resources.[16] It was also necessary to organize courses and exams for the numerous war veterans coming back from the front and for new students, with more than a half of the teaching personnel blocked beyond theGothic Line:[15] and in performing all those task Cafiero, jointly with few others and working as an adjunct professor of "Esercitazioni di Matematiche", was an outstanding collaborator ofRenato Caccioppoli andCarlo Miranda.[17]
Also in 1944 he married Jole Giorgini, his lifelong companion, and soon after they had a daughter, Anna.[7]
Due to the scarce possibilities of being hired permanently by the Faculty of Sciences at that time, he accepted a position as adjunctassistant professor to the chair ofFinancial Mathematics,[18] working with Luigi Lordi first at theIstituto Universitario Navale and then to the Faculty of Economics and Business, where he was appointed fullassistant professor in June 1949.[19] Nonetheless, his ties with the Faculty of Sciences remained strong, being employed there as an adjunct professor of "Esercitazioni di Matematiche" several times, during those years:[20] he was likewise assigned to several other courses related to Financial Mathematics by the Istituto Universitario Navale and by the Faculty of Business and Economics.[20][21]
The scientific aspect of the collaboration with the Faculty of Sciences was nonetheless very intense,[20] leading him to the "libera docenza" in March 1951, and to a full professorship chair in 1953:[22][23] during this period, his scientific activity was done side by side at first with Carlo Miranda and later with Renato Caccioppoli, who found in him a dear pupil and friend.[24]
Apart from the silver medal awarded him for his valor acts during the military service,[12] the importance of his scientific achievements was acknowledged several times. In 1952 he received the Tenore Prize of the Accademia Pontaniana for a memoir on the theory of integration,[1] later published as the paper (Cafiero 1953) and the monograph (Cafiero 1953a). On May 25, 1954 he was electedresident corresponding member of theAccademia Gioenia di Catania during his stay at the University of Catania, and becamenon resident corresponding member from November 16, 1956 on, after his moving to Pisa and then to Naples.[34]
Ma è subito dopo la seconda guerra mondiale che ilprocesso di astrattizzazione della teoria della misura e dell'integrale si completa in modo definitivo. A ciò contribuironoPaul Halmos negli U.S.A. eRenato Caccioppoli, Federico Cafiero (1914–1980) ed altri in Italia.[35]
ComeAndreotti ancheStampacchia non poté venire subito a Pisa e così io fui felice di avere con me un altro valoroso allievo di Renato Caccioppoli, Federico Cafiero, che restò a Pisa poco tempo, ma vi lasciò una forte traccia e formò il suo valido continuatore Giorgio Letta.[36]
The papers of Federico Cafiero listed in this section are also included in his "Opere scelte" (Cafiero 1996), which collects all his published notes and one of his books.
Cafiero, Federico (1953a),Funzioni additive d'insieme e integrazione negli spazi astratti [Additive set functions and integration in abstract spaces] (in Italian),Napoli:Libreria Editrice Liguori, p. 178,MR0056671,Zbl0050.27801, is the prize-winning first monograph where Federico Cafiero states and proves his convergence theorem.
Cafiero, Federico (1959),Misura e integrazione [Measure and integration], Monografie matematiche delConsiglio Nazionale delle Ricerche (in Italian), vol. 5,Roma: Edizioni Cremonese, pp. VII+451,MR0215954,Zbl0171.01503, is a definitive monograph on integration and measure theory: the treatment of the limiting behaviour of the integral of various kinds ofsequences of measure-related structures (measurable functions,measurable sets, measures and their combinations) is somewhat conclusive.
Cafiero, Federico (1996),Opere scelte, a cura del Dipartimento di matematica e applicazioni R. Caccioppoli dell'Università degli studi di Napoli Federico II e con il contributo dell'Accademia Pontaniana e dei dipartimenti di matematica delle università di Catania, di Napoli e di Pisa (in Italian),Napoli:Giannini Editore, p. 701. Federico Cafiero's "Selected works", including all his published papers, three postcards from his master Renato Caccioppoli concerning his research and his book "Lezioni sulla teoria delle funzioni di variabili reali" (English:"Lectures on the theory of functions of real variables").
^See (Letta 1981, p. 347), (Miranda 1980–1981, p. 9) and (Roghi 2005, p. 13): Letta and Roghi clearly state the academic year, while Miranda states that he won the scholarship "subito dopo" i.e. "soon after" earning his Laurea degree. Roghi gives many other details about the scholarship, including the names of other winners and its amount, which was 5000Italian liras.
^According toLetta (1981, p. 347), who reports also that Cafiero was confirmed in the job for the three following years.Miranda (1980–1981, p. 9) presents a slightly different version, referring that he was appointed instructor of the course of "Esercitazioni di Matematiche" (i.e. "Exercises in mathematics") by the Faculty of sciences. However, the version of Letta has been followed since it is more circumstantial, offering more details.
^See (Letta 1981, p. 347) and (Miranda 1980–1981, p. 9): unlike the former one, this last source does not state the duration of Cafiero's stay in Africa.
^Description of the state the Institute at the time, as reported here, is taken from the brief but vivid description given byMiranda (1980–1981, p. 9).
^Miranda (1980–1981, p. 9) remarks precisely that, to perform all those tasks, they could only rely on two old janitors, and that the funds available for the institution were trifling.
^This highly positive assessment of his work during those years is due toMiranda (1980–1981, p. 9) himself.
^Miranda (1980–1981, p. 9) details briefly but comprehensively these early career steps, whileLetta (1981, p. 347) only outlines them.De Angelis & Sbordone (1999, p. 29) state precisely the academic years and the course held by Cafiero at the Institute.
^De Angelis & Sbordone (1999, p. 29) state that he was a lecturer (the exact Italian academic rank was "professore incaricato") of "Matematica generale" (Free English translation:"General mathematics") for the academic year 1952/1953.
^The "free professorship" (in a literal free English translation) was an academic title similar to theGerman "Habilitation", no longer in force in Italy since 1970.
^See (Miranda 1980–1981, p. 10): Miranda precisely uses the term "carissimo", which in the Italian language means more thandear (caro) and less thandearest (il più caro).
^See the announce on theBollettino UMI (1953, p. 471), reporting also the names of other winners and of the judging committee.
^SeeLetta (1981, p. 347), (Miranda 1980–1981, p. 10) and the announce on theBollettino UMI (1953, p. 472), "Nomine di nuovi professori straordinari" section: Letta and Miranda precisely state the month and the year of his appointment.
^See (Letta 1981, p. 347), (Marino 2008, p. 2), (Maugeri 1994, p. 179) and (Miranda 1980–1981, p. 10). Letta, Maugeri and Miranda precisely state the month and the year of his arrival: on the other hand, Maugeri and Marino refer also that he substituted Vincenzo Amato (1881–1963), retired during theacademic year 1951–1952.
^According toLetta (1981, p. 348), who refers also that he was awarded a gold medal for the role he played in the construction of a newelectronic computer at the university.
^(English translation) "But it was immediately after the second world war that theprocess of abstraction of measure and integration theory was completed in a definitive manner. Paul Halmos in the U.S.A. and Renato Caccioppoli, Federico Cafiero (1914–1980) and others in Italy were the main contributors". TheItalic type emphasis is due to the Author himself.
^(English translation) "As Andreotti also Stampacchia could not come immediately to Pisa therefore I was happy to have with me another valiant pupil of Renato Caccioppoli, Federico Cafiero, who was in Pisa for a short time but left a strong trace and formed his valid successor Giorgio Letta."
Accademia Pontaniana (2015),Annuario della Accademia Pontaniana 2015 (DLXXIII dalla fondazione)(PDF) (in Italian), Napoli: Nella Sede dell'Accademia, p. 180, archived fromthe original(PDF) on 6 March 2015, retrieved8 March 2015. The "Yearbook 2015" of the Accademia Pontaniana, published by the academy itself and describing its past and present hierarchies and its activities. It also gives some notes on its history, the full list of its members and other useful information.
de Lucia, Paolo; Sbordone, Carlo (1996),Presentazione (in Italian), p. 9 of the book (Cafiero 1996). The short "Introduction" to Cafiero's selected works by its editors: it includes also a few biographical data.
De Angelis, P. L.;Sbordone, C., eds. (1999), "Federico Cafiero",Matematici all'Istituto Universitario Navale (1926 – 1976) [Mathematicians at the Istituto Universitario Navale (1926–1976)] (in Italian), Napoli:Istituto Universitario Navale/RCE Edizioni, pp. 29–36. The chapter on Cafiero in a book collecting brief biographical sketches and bibliographies of scientific production of the mathematicians who worked at theParthenope University of Naples, during their stay at the renowned Neapolitan University.
Faedo, Sandro (1986), "Leonida Tonelli e la scuola matematica pisana", in Montalenti, G.;Amerio, L.; Acquaro, G.; Baiada, E.; et al. (eds.),Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei (in Italian), vol. 77, Roma:Accademia Nazionale dei Lincei, pp. 89–109, archived fromthe original on 23 February 2011, retrieved12 February 2013. "Leonida Tonelli and the Pisa mathematical school" is a survey of the work of Tonelli inPisa and his influence on the development of the school, presented at theInternational congress in occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985). The Author was one of his pupils and, after his death, held his chair of mathematical analysis at theUniversity of Pisa, becoming dean of the faculty of sciences and then rector: he exerted a strong positive influence on the development of the university.
Letta, Giorgio (1981), "Federico Cafiero",Bollettino dell'Unione Matematica Italiana, Sezione A, Serie V (in Italian),18 (2):347–355,MR0618356,Zbl0457.01006. Includes a publication list.
Maugeri, Antonino (1994),"Dal seminario al dipartimento" [From the seminar to the department],Le Matematiche (in Italian),XLIX (I):175–183, is a short history of the Department of Mathematics of the University of Catania: the Author briefly describes the positive contribution of Federico Cafiero to the research and teaching activity during his stay.
Società Nazionale di Scienze Lettere e Arti in Napoli (2014),Annuario della Società Nazionale di Scienze Lettere e Arti in Napoli – 2014(PDF) (in Italian), Napoli: Società Nazionale di Scienze Lettere e Arti in Napoli, p. 82, archived fromthe original(PDF) on 3 March 2016, retrieved8 March 2015. The "Yearbook 2014" of the Società Nazionale di Scienze Lettere e Arti in Napoli, published by the society itself and describing its past and present hierarchies, and its activities. It also reports some notes on its history, the full list of its members and other useful information.
de Lucia, Paolo (1988), "Analisi reale e teoria della misura a Napoli: R. Caccioppoli, C. Miranda e F. Cafiero", inSocietà Nazionale di Scienze, Lettere ed Arti in Napoli (ed.),Seduta inaugurale dell'anno accademico 1988 (in Italian),Napoli: Francesco Giannini e Figli, pp. 23–33. "Real analysis and measure theory in Naples: R. Caccioppoli, C. Miranda and F. Cafiero" (English translation of the title) is the opening address of the 1988 academic year of theSocietà Nazionale di Scienze, Lettere ed Arti in Napoli: it describes the contributions of Caccioppoli, Miranda and Cafiero to real analysis and measure theory during their stay in Naples.
de Lucia, Paolo (2004) [1999], "Teoria della Misura a Napoli: Renato Caccioppoli", in Alvino, A.; Carbone, L.;Sbordone, C.; Trombetti, G. (eds.),In ricordo di Renato Caccioppoli [In memoriam Renato Caccioppoli] (in Italian) (2nd printing ed.), Napoli: Giannini, p. 124,MR1306300,Zbl0793.01019 (reviews of the symposium papers, see below): a collection of papers detailing his personality and his research, including the introduction to his "Opere scelte" (Selected works), a list of contributions from the "International Symposium Renato Caccioppoli" held in Napoli on September 20–22, 1989, a conference held by Caccioppoli himself and related letters byCarlo Miranda, Giovanni Prodi andFrancesco Severi. This paper, "Measure theory in Naples: Renato Caccioppoli", appeared in the proceedings of the symposium, details Cacioppoli's and Cafiero's contributions to the development of Measure Theory.
Letta, Giorgio (2013),Argomenti scelti di Teoria della Misura [Selected topics in Measure Theory], Quaderni dell'Unione Matematica Italiana (in Italian), vol. 54,Bologna:Unione Matematica Italiana, pp. XI+183,ISBN978-88-371-1880-8,Zbl1326.28001, is, according to its Author, an exposition of classical topics in Measure Theory that, despite their conceptual relevance and potential applicability, are rarely taught in current (2012) Italian university courses.
