Random variable

Definition

A Random variable is a measurable map from a probability space to any measurable space

Let $(\Omega,\mathcal{A},\mathbb{P})$ be a probability space and let $\Epsilon:\Omega\rightarrow\mathbb{R}$ be a random variable

(that means it is a measurable map FROM a probability space to a measurable space recall)

Then:

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TODO: Finish this because it's iffy

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