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
Function
Measure
Real measure
Euclidean real measure
Complex measure
Basic measure
Unsigned basic measure
Outer measure
Stieltjes outer measure
Lebesgue-Stieltjes-measurable set
Stieltjes sigma-algebra
Definition D1861
Stieltjes measurable space
Formulation 0
Let $F : \mathbb{R} \to \mathbb{R}$ be a D4364: Real function such that
(i) $F$ is a D3249: Right-continuous function
(ii) $F$ is a D5321: Standard-isotone basic real function
An D548: Ordered pair $M = (\mathbb{R}, \mathcal{S})$ is a Stieltjes measurable space with respect to $F$ if and only if
(1) $\mathbb{R}$ is the D282: Set of real numbers
(2) $\mathcal{S}$ is the D1860: Stieltjes sigma-algebra on $\mathbb{R}$ with respect to $F$
Children
Stieltjes measure