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arXiv · 2502.05083

Discrete probability spaces revisited

Christian Döbler
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Abstract

We give an elementary proof of the known fact that every probability measure, defined on an arbitrary $\sigma$-field on a countable sample space $\Omega$, may in fact be extended to a probability measure on the power set of $\Omega$. This result is further discussed and motivated in the context of discrete random variables.

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Christian Döbler. 2025-02-07. Discrete probability spaces revisited. https://arxiv.org/abs/2502.05083

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