Unsigned basic expectation

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Unsigned basic expectation

Formulation 0

Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X : \Omega \to [0, \infty]$ is a D5101: Random unsigned basic number on $P$

The expectation of $X$ on $P$ is the D1699: Basic number \begin{equation} \mathbb{E}_{\mathbb{P}} X : = \int_{\Omega} X \, d \mathbb{P} \end{equation}

Child definitions

» D5102: Basic expectation

Results

» R3517: Unsigned basic expectation zero iff random number almost surely zero

» R3595: Probabilistic Tonelli's theorem

» R5301: Random unsigned basic number has zero correlation with the empty indicator