Abstract
The convergence of an infinite series\(\sum _{n=1}^\infty X_n\) is a tail event.
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Notes
- 1.
Theorem8.6 is a stronger statement than Kolmogorov’s classical strong law. It is due to Marcinkiewicz and Zygmund (1937) : Sur les fonctions indépendentes,Fund. Math.29, 60–90., but clearly contains the classical law as a special case.
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Department of Mathematics, University of Arizona, Tucson, AZ, USA
Rabi Bhattacharya
Department of Mathematics, Oregon State Univeristy, Corvallis, OR, USA
Edward C. Waymire
- Rabi Bhattacharya
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- Edward C. Waymire
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Correspondence toRabi Bhattacharya.
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Bhattacharya, R., Waymire, E.C. (2016). Random Series of Independent Summands. In: A Basic Course in Probability Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-47974-3_8
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