Baire set


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Baire set

[′ber ‚set]
(mathematics)
A member of the smallest sigma algebra containing all closed, compact subsets of a topological space.
References in periodicals archive ?
Let Ba denote the [sigma]-algebra of Baire sets in [OMEGA], which is the [sigma]-algebra generated by the class Z of all zero sets of bounded continuous positive functions on [omega].
The elements of the [sigma]-algebra generated by zero-sets are called Baire sets and the elements of the [sigma]-algebra generated by closed sets are called Borel sets; B(X)and [B.sub.0](X) are the classes of Borel and Baire subsets of X and [M.sub.[sigma]](X) denotes the class of all scalar-valued, countably additve Baire measures on X.
Subjects covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, with papers on such topics as the strength of some combinatorial principles related to Ramsey's theorem for pairs, absoluteness for universally Baire sets and the uncountable, modaic definability of ordinals, eliminating concepts, rigidity and bi-interpretability in hyperdegrees, fundamental issues of degrees of unsolvability, a "tt" version of the Posner-Robinson theorem, and prompt simplicity, array computability and cupping.