functions. They were introduced by René-Louis Baire in 1899. A Baire set is a set whose characteristic function is a Baire function. Baire functions of...

les fonctions de variables réelles ("On the Functions of Real Variables") in 1899. The son of a tailor, Baire was one of three children from a poor working-class...

is said to be a Baire space if countable unions of closed sets with empty interior also have empty interior. According to the Baire category theorem...

compactly supported continuous function on such a space is integrable with respect to any finite Baire measure. Every Baire set is a Borel set. The converse...

shows that the Dirichlet function is a Baire class 2 function. It cannot be a Baire class 1 function because a Baire class 1 function can only be discontinuous...

A Baire one star function is a type of function studied in real analysis. A function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is in class...

The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient...

set. This would contradict the Baire category theorem: because the reals form a complete metric space, they form a Baire space, which cannot be meager...

Measurable function: the preimage of each measurable set is measurable. Borel function: the preimage of each Borel set is a Borel set. Baire function called...

The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899. Assume throughout that X...