ABSTRACT
This chapter considers measurable functions of more than one variable, that is, functions on measurable spaces of the form X: = X1 × X2 × · · · × Xk with appropriate σ-algebras and measures on them. It focuses for the case of k = 2. Thus, the idea is to construct a new σ-algebra and a measure on X1 × X2 using the measure spaces X1 and X2, and see how integration on the product space is related to the integration on the component spaces. The chapter shows that the existence of a product measure with the required properties will be guaranteed whenever μ1 and μ2 are σ-finite measures. It also discusses Fubini's theorem.
