ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D5102
Basic expectation

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) $$\mathbb{E} |X| < \infty$$
The expectation of $X$ on $P$ is the D1699: Basic number $$\mathbb{E}_{\mathbb{P}} X : = \mathbb{E}_{\mathbb{P}} X^+ - \mathbb{E}_{\mathbb{P}} X^-$$
Children
 ▶ D2015: Random real number moment
Results
 ▶ R4577: Countable indicator partition of complex expectation in terms of pullback events ▶ R5282: Expectation of a random fraction need not equal fraction of expectations ▶ R4777: Expectation of bounded random real number is within the bounding interval ▶ R3516: Signed basic expectation of almost surely zero random number is zero