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Random Maps, Distribution, and Mathematical Expectation

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A Basic Course in Probability Theory

Part of the book series: Universitext ((UTX))

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Abstract

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

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Notes

  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.

Author information

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

Authors
  1. Rabi Bhattacharya
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  2. Edward C. Waymire
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Corresponding author

Correspondence to Rabi Bhattacharya .

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© 2016 Springer International Publishing AG

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Bhattacharya, R., Waymire, E.C. (2016). Random Maps, Distribution, and Mathematical Expectation. In: A Basic Course in Probability Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-47974-3_1

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