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Riemann–Stieltjes integral

In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes. It serves as an instructive and useful precursor of the Lebesgue integral, and an invaluable tool in unifying equivalent forms of…

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Overview

Formal definition

Properties

Application to probability theory

Application to functional analysis

Existence of the integral

Generalization

Examples and special cases

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Riemann–Stieltjes integral

Nodes50
Edges49
Triples48
Avg. degree1.96
Density0.04
Components1

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Riemann–Stieltjes integral

Top relations

related to Application to functional analysis · 8
Riemann–Stieltjes integral → Banach, Hilbert, In, Later, Riemann, Riesz's, Stieltjes, The Riemann
related to Generalization · 7
Riemann–Stieltjes integral → An, Banach, If, Lebesgue, Riemann, Stieltjes, The Riemann
related to Cavalieri integration · 6
Riemann–Stieltjes integral → Cavalieri, Cavalieri's, For, Riemann, Stieltjes, The
related to Differentiable g · 5
Riemann–Stieltjes integral → Given, Let, Riemann, Stieltjes, Then
related to Geometric interpretation · 5
Riemann–Stieltjes integral → If, Riemann, Stieltjes, The, The Riemann-Stieltjes
related to Darboux sums · 4
Riemann–Stieltjes integral → Darboux, For, Stieltjes, The Riemann
related to Generalized Riemann–Stieltjes integral · 4
Riemann–Stieltjes integral → Pε, Riemann, Specifically, Stieltjes
related to Formal definition · 3
Riemann–Stieltjes integral → Its, Stieltjes, The Riemann
related to Riemann integral · 3
Riemann–Stieltjes integral → Riemann, Stieltjes, The
related to Properties · 2
Riemann–Stieltjes integral → Stieltjes, The Riemann

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Important terminology

integral stieltjes riemann displaystyle continuous function bounded generalization respect variation mathematical analysis cases integration definition probability isbn functions exists fence

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Riemann–Stieltjes integralis ageneralization of the Riemann integral0.90text
Riemann–Stieltjes integralrelated to Application to functional analysisThe Riemann0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisStieltjes0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisRiesz's0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisBanach0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisRiemann0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisLater0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisHilbert0.60section
Riemann–Stieltjes integralrelated to Application to functional analysisIn0.60section
Riemann–Stieltjes integralrelated to Cavalieri integrationCavalieri's0.60section
Riemann–Stieltjes integralrelated to Cavalieri integrationRiemann0.60section
Riemann–Stieltjes integralrelated to Cavalieri integrationStieltjes0.60section

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