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

**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}

▾ 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

▾ 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

Formulation 0

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

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}

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

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