Probability Measure is Subadditive

Theorem

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Then $\Pr$ is a subadditive function.


Proof

By definition, a probability measure is a measure.

The result follows from Measure is Subadditive

$\blacksquare$

This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.