Measure and topology

Hari Bercovici, Arlen Brown and Carl Pearcy
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Hari Bercovici: Indiana University, Department of Mathematics
Arlen Brown: Indiana University, Department of Mathematics
Carl Pearcy: Texas A&M University, Department of Mathematics

Chapter Chapter 7 in Measure and Integration, 2016, pp 167-182 from Springer

Abstract: Abstract Given a topological space -topological space topological space X, there is a natural σ $$\sigma$$ -algebra -Borel σ $$\sigma$$ -algebra of subsets of X, namely the σ $$\sigma$$ -algebra B X of Borel sets. When X is locally compact space -topological -locally compact (that is, every point has a relatively compact neighborhood) another useful σ $$\sigma$$ -algebra is the σ $$\sigma$$ -algebra generated by the compact G δ subsets of X. This collection is called the σ $$\sigma$$ -algebra of Baire sets Baire set and is Ba X : Baire σ $$\sigma$$ -algebra denoted Ba X . The σ $$\sigma$$ -algebra Ba X is defined the same way for arbitrary topological spaces, but it is not so useful when X is not locally compact.

Keywords: Baire Set; Arbitrary Topological Space; Continuous Function Space; Riesz Representation Theorem; Moment Sequence (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-29046-1_7

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