ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Measurable space
Definition D1158
Measure space
Formulation 0
A D5107: Triple $M = (X, \mathcal{F}, \mu)$ is a measure space if and only if
(1) $(X, \mathcal{F})$ is a D1108: Measurable space
(2) $\mu$ is an D85: Unsigned basic measure on $(X, \mathcal{F})$
Subdefinitions
D1159: Probability space
Children
D4248: Almost everywhere constant map
D2940: Measure-preserving endomorphism
D1159: Probability space
D1732: Pushforward measure
Results
R4927: Binary partition additivity of unsigned basic measure
R1234: Borel-Cantelli lemma
R3645: Countable partition additivity of unsigned basic measure
R979: Countable subadditivity of measure
R4841: Finite disjoint additivity of probability measure
R976: Finite disjoint additivity of unsigned basic measure
R4926: Finite partition additivity of unsigned basic measure
R4445: Inclusion-exclusion principle for probability of binary union
R4318: Inclusion-exclusion principle for unsigned basic measure of binary union
R4317: Inclusion-exclusion principle for unsigned basic measure of ternary union
R975: Isotonicity of unsigned basic measure
R3970: Measure of finite union finite iff measure of all sets in union finite
R3969: Measure of intersection finite if measure of at least one set finite
R4277: Measure of measurable set complement
R978: Measure of set difference
R4443: Measure of symmetric difference of set and subset
R4453: Probability of symmetric difference of event and subevent
R982: Sequential continuity of measure from below