Difference between revisions of "Borel set, criterion for a"
From Encyclopedia of Mathematics
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| − | A necessary and sufficient condition for an [[A-set| | + | {{TEX|done}} |
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| + | A necessary and sufficient condition for an [[A-set|$\mathcal{A}$-set]] in a complete separable [[metric space]] to be a [[Borel set]]. Two criteria can be stated as follows: 1) its complement must also be an $\mathcal{A}$-set (Suslin's criterion); and 2) it can be represented as the union of non-intersecting components (Luzin's criterion). | ||
Latest revision as of 21:57, 19 December 2014
A necessary and sufficient condition for an $\mathcal{A}$-set in a complete separable metric space to be a Borel set. Two criteria can be stated as follows: 1) its complement must also be an $\mathcal{A}$-set (Suslin's criterion); and 2) it can be represented as the union of non-intersecting components (Luzin's criterion).
How to Cite This Entry:
Borel set, criterion for a. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_set,_criterion_for_a&oldid=13153
Borel set, criterion for a. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_set,_criterion_for_a&oldid=13153
This article was adapted from an original article by A.G. El'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article