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