Probability pp 129-305 | Cite as

Mathematical Foundations of Probability Theory

  • A. N. Shiryayev
Part of the Graduate Texts in Mathematics book series (GTM, volume 95)


The models introduced in the preceding chapter enabled us to give a probabilistic-statistical description of experiments with a finite number of outcomes. For example, the triple (Ω, A, P) with
$$\Omega = \left\{ {\omega :\omega = \left( {{a_1},...,\left. {{a_n}} \right)} \right.} \right.,\;{a_i}\; = \;\left. {0,1} \right\},\;A\; = \;\left\{ {A:\;A \subseteq \Omega } \right\}$$
and \(p\left( \omega \right)\; = \;{p^{\sum {a_i}}}{q^{n - \sum {a_i}}}\) is a model for the experiment in which a coin is tossed n times “independently” with probability p of falling head. In this model the number N(Ω) of outcomes, i.e. the number of points in Ω, is the finite number 2n.


Probability Measure Measurable Space Conditional Expectation Random Element Mathematical Foundation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • A. N. Shiryayev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowUSSR

Personalised recommendations