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Basic expectation
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to [-\infty, \infty]$ is a D4381: Random basic number on $P$
(ii) \begin{equation} \mathbb{E} |X| < \infty \end{equation}
The expectation of $X$ on $P$ is the D1699: Basic number \begin{equation} \mathbb{E}_{\mathbb{P}} X : = \mathbb{E}_{\mathbb{P}} X^+ - \mathbb{E}_{\mathbb{P}} X^- \end{equation}
Child definitions
» D2015: Random real number moment
Results
» R3516: Signed basic expectation of almost surely zero random number is zero
» R4577: Countable indicator partition of complex expectation in terms of pullback events
» R4777: Expectation of bounded random real number is within the bounding interval
» R5282: Expectation of a random fraction need not equal fraction of expectations