Product measures

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 8 in Measure and Integration, 2016, pp 183-201 from Springer

Abstract: Abstract In this chapter we treat an additional important topic in the theory of measure and integration concerning one way that new S ×T: product σ $$\sigma$$ -algebra measures can be constructed from old ones. If (X, S) and (Y, T) are measurable spaces, then a set of the form E × F, where E ∈ S and F ∈ T, is called a measurable rectangle measurable rectangle rectangle -measurable in X × Y. σ $$\sigma$$ -algebra -product The σ $$\sigma$$ -algebra of subsets of X × Y generated by the collection of all measurable rectangles is denoted by S ×T, and the space X × Y measurable space -product equipped with the product σ $$\sigma$$ -algebra S ×T is a measurable space called the product of (X, S) and (Y, T).

Keywords: Measurable Rectangles; Free Measure Space; Product Probability Space; Cylinder Measure; General Integrable Function (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-29046-1_8

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DOI: 10.1007/978-3-319-29046-1_8

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