# A-operation

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operation A set-theoretical operation, discovered by P.S. Aleksandrov  (see also , ). Let be a system of sets indexed by all finite sequences of natural numbers. The set where the union is over all infinite sequences of natural numbers, is called the result of the -operation applied to the system .

The use of the -operation for the system of intervals of the number line gives sets (called -sets in honour of Aleksandrov) which need not be Borel sets (see -set; Descriptive set theory). The -operation is stronger than the operation of countable union and countable intersection, and is idempotent. With respect to -operations, the Baire property (of subsets of an arbitrary topological space) and the property of being Lebesgue measurable are invariant.

How to Cite This Entry:
A-operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=A-operation&oldid=16633
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