ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
Definition D5103
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}
Children
Basic expectation
Results
Probabilistic Tonelli's theorem
Random unsigned basic number has zero correlation with the empty indicator
Unsigned basic expectation zero iff random number almost surely zero