Random variable

Definition

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

Let [ilmath](\Omega,\mathcal{A},\mathbb{P})[/ilmath] be a probability space and let [ilmath]\Epsilon:\Omega\rightarrow\mathbb{R} [/ilmath] 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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