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
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Ringoid
▼ Semiring
▼ Ring
▼ Left ring action
▼ Module
▼ Vector space
▼ Vector space seminorm
▼ Vector space norm
▼ Normed vector space
▼ Bounded set
▼ Bounded map
▼ Constant-bounded map
▼ Constant-bounded function
▼ Finite measure
Definition D198
Probability measure
Formulation 0
Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
An D85: Unsigned basic measure $\mu : \mathcal{F} \to [0, \infty]$ is a probability measure on $M$ if and only if \begin{equation} \mu(X) = 1 \end{equation}
Children
▶ D2282: Set of probability measures
Results
▶ R4739: Binary subadditivity of probability measure
▶ R2093: Countable subadditivity of probability measure
▶ R4738: Finite subadditivity of probability measure
▶ R2090: Isotonicity of probability measure
▶ R2092: Sequential continuity of probability measure from above
▶ R2091: Sequential continuity of probability measure from below
▶ R3938: Upper and lower bounds for codomain set of probability measure