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Borel set

In mathematics, the Borel sets of a topological space are a particular class of "well-behaved" subsets of that space. For example, whereas an arbitrary subset of the real numbers might fail to be Lebesgue measurable, every Borel set of reals is universally measurable. Which sets are Borel can be specified in a number of equivalent ways. Borel sets are…

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Overview

Generating the Borel algebra

Standard Borel spaces and Kuratowski theorems

Non-Borel sets

Alternative non-equivalent definitions

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Borel set

Nodes66
Edges65
Triples53
Avg. degree1.97
Density0.030303
Components1

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Borel set

Top relations

related to Further reading · 24
Borel set → An Invitation, Baire, Borel, Brooks, Classical Descriptive Set Theory, Cole, Graduate, Halsey Royden, Kechris, Math, Measure, Nostrand Co, Paul, Polish, Prentice Hall, Probability, Real Analysis, Richard Dudley, Sect, See
related to External links · 12
Borel set → Archived, Borel, Borel Sets, EMS Press, Encyclopedia, Eric, Formal, Mathematics, MathWorld, Mizar, Wayback Machine, Weisstein
related to Alternative non-equivalent definitions · 8
Borel set → According, Borel, Hausdorff, It, Norberg, Paul Halmos, This, Vervaat
related to Standard Borel spaces and Kuratowski theorems · 8
Borel set → Borel, George Mackey, However, Let, Mackey's, The, The Borel, There
is a · 1
Borel set → inverse image f

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Important terminology

borel sets displaystyle set space topological open σ-algebra number defined algebra countable subsets subset measurable spaces ordinal definition measure theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Borel setis ainverse image f0.90text
Borel setrelated to Alternative non-equivalent definitionsAccording0.60section
Borel setrelated to Alternative non-equivalent definitionsPaul Halmos0.60section
Borel setrelated to Alternative non-equivalent definitionsHausdorff0.60section
Borel setrelated to Alternative non-equivalent definitionsBorel0.60section
Borel setrelated to Alternative non-equivalent definitionsNorberg0.60section
Borel setrelated to Alternative non-equivalent definitionsVervaat0.60section
Borel setrelated to Alternative non-equivalent definitionsThis0.60section
Borel setrelated to Alternative non-equivalent definitionsIt0.60section
Borel setrelated to External linksBorel0.60section
Borel setrelated to External linksEncyclopedia0.60section
Borel setrelated to External linksMathematics0.60section

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