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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).

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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=35729

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

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