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Lebesgue's decomposition theorem

In mathematics, more precisely in measure theory, the Lebesgue decomposition theorem provides a way to decompose a measure into two distinct parts based on their relationship with another measure.

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Overview

Formal Statement

Measurable space
Σ-finite Sigma-finite measure
Signed measures Signed measure
Absolutely continuous Absolute continuity (measure theory)
Singular Singular measure
Positive measure
Complex measure
Radon–Nikodym theorem
Borel measure
Discrete measure
Cantor measure
Probability measure
Real line
Cumulative distribution function
Cantor function

Related concepts

Stochastic processes
Lévy–Itō decomposition
Lévy processes Lévy process
Brownian motion
Compound Poisson process
Square integrable
Martingale Martingale (probability theory)

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Map overview Semantic statistics

Lebesgue's decomposition theorem

Nodes28

Edges27

Triples10

Avg. degree1.93

Density0.071429

Components1

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Lebesgue's decomposition theorem

Top relations

related to Refinement · 10

Lebesgue's decomposition theorem → First, If, Lebesgue, Lebesgue's, Nikodym, Omega, Radon, Sigma, That, There

Important terminology Word statistics

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Important terminology

decomposition displaystyle theorem measure singular mu continuous lebesgue mathematics theory sigma measures absolutely radon nikodym lambda real isbn mr ll

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Lebesgue's decomposition theorem	related to Refinement	Lebesgue's	0.60	section
Lebesgue's decomposition theorem	related to Refinement	First	0.60	section
Lebesgue's decomposition theorem	related to Refinement	Lebesgue	0.60	section
Lebesgue's decomposition theorem	related to Refinement	Radon	0.60	section
Lebesgue's decomposition theorem	related to Refinement	Nikodym	0.60	section
Lebesgue's decomposition theorem	related to Refinement	That	0.60	section
Lebesgue's decomposition theorem	related to Refinement	Omega	0.60	section
Lebesgue's decomposition theorem	related to Refinement	Sigma	0.60	section
Lebesgue's decomposition theorem	related to Refinement	There	0.60	section
Lebesgue's decomposition theorem	related to Refinement	If	0.60	section

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Min side: 3

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