This chapter is devoted to measures and integrals on product spaces. The first two sections contain the basic facts about product measures and about the evaluation of integrals on product spaces; the last section contains some applications.
KeywordsLebesgue Measure Measure Space Product Space Product Measure Borel Subset
Unable to display preview. Download preview PDF.
- The basic facts given above on products of a finite number of σ-finite measure spaces can be found in almost every book on measure and integration. The theory of products of an infinite number of measure spaces is needed for the study of probability and can be found, for instance, in Halmos .Google Scholar
- See Bledsoe and Morse  for a more delicate and more powerful theory of measurability in product spaces.Google Scholar
- The proof of Proposition 1.4.8 indicated in Exercise 5.3.8 was shown to me by Charles Rockland and (independently) by Lee Rubel.Google Scholar