In the spirit of a refresher, we begin with an overview of the measure–theoretic framework for probability.

1. 1.

   With the exception of properties for “complements” and “continuity from above,” these and the aforementioned consequences can be checked to hold for any measure.

2. 2.

   Throughout, this square-bracket notation will be used to denote events defined by inverse images.

3. 3.

   For an application see Bhattacharya, R.N., Kim, H., Majumdar, M.K. (2015): Sustainability in the Stochastic Ramsey Model,J. Quant. Econ.13, 169–184.

Authors and Affiliations

1. Department of Mathematics, University of Arizona, Tucson, AZ, USA

   Rabi Bhattacharya

2. Department of Mathematics, Oregon State Univeristy, Corvallis, OR, USA

   Edward C. Waymire

Corresponding author

Correspondence toRabi Bhattacharya.

Reprints and permissions

© 2016 Springer International Publishing AG

Policies and ethics