ABSTRACT
In this chapter we provide the first application of the extension theorems of Chapter 6. Other results of this type will be developed in the later chapters. The application here is to “product spaces” which are in effect, multi-dimensional versions of the measures spaces addressed so far. For example, the 2-dimensional Euclidean space ℝ2 is a product space ℝ × ℝ. Not surprisingly, the development above for Lebesgue or Borel measures on ℝ can be generalized to produce Lebesgue, Borel measures or general measure spaces on ℝ2 or ℝ n .
