In mathematics, a Baire set is an element of the smallest σ–algebra containing all compact "Gδ" sets. On a compact space, the Baire sets form the smallest σ–algebra such that all bounded continuous functions to the real line are
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Universally Baire set — In the mathematical field of descriptive set theory, a set of reals (or subset of the Baire space or Cantor space) is called universally Baire if it has a certain strong regularity property. Universally Baire sets play an important role in Ω… … Wikipedia
Baire measure — A Baire measure is a measure on the σ algebra of Baire sets of a topological space. In spaces that are not metric spaces, the Borel sets and the Baire sets may differ. In this context, Baire measures are used because they connect to the… … Wikipedia
Baire one star function — is a term from real analysis. A function f: mathbb{R} o mathbb{R} is in class Baire* one, written f in mathbf{B}^{*} {1}, and is called a Baire one star function, if for each perfect set P in mathbb{R}, there is an open interval I in mathbb{R},… … Wikipedia
Baire space — In mathematics, a Baire space is a topological space which, intuitively speaking, is very large and has enough points for certain limit processes. It is named in honor of René Louis Baire who introduced the concept. Motivation In an arbitrary… … Wikipedia
Baire space (set theory) — In mathematics field of set theory, especially descriptive set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology. This space is commonly used in descriptive set theory, to the extent that its… … Wikipedia
Baire category theorem — The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space. Statement of the theorem *(BCT1) Every… … Wikipedia
Baire function — In mathematics, Baire functions refer to certain sets of functions. They are studied in several fields of mathematics, including real analysis and topology.Baire functions of class n , for any ordinal number n , are a set of real valued functions … Wikipedia
Baire, René-Louis — ▪ French mathematician born January 21, 1874, Paris, France died July 5, 1932, Chambéry French mathematician whose study of irrational numbers (irrational number) and the concept of continuity of functions that approximate them greatly… … Universalium
René-Louis Baire — (January 21 1874 ndash; July 5 1932), was a French mathematician. He was born in Paris, France and died in Chambéry, France.Dogged by ill health, and spending time alternating between low level teaching in lycées and work in universities, he was… … Wikipedia
Borel set — In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named… … Wikipedia
