ABSTRACT
In this chapter we retain the notation introduced in Chapter 1 but unless otherwise indicated, Ω ⊂ ℝ n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5432.tif"/> will stand for an open set and we will consider the measure space ( Ω , B , μ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5433.tif"/> where B https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5434.tif"/> stands for the Borel σ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5435.tif"/> -algebra of subsets of Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5436.tif"/> , μ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5437.tif"/> denotes the restriction of the Lebesgue measure to the Borel σ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5438.tif"/> -algebra of Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5439.tif"/> and φ : Ω × [ 0 , ∞ ) → [ 0 , ∞ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781498762618/4882778a-ba8d-4a3b-a129-38b97b5fc627/content/eq5440.tif"/>
