Lebesgue Equivalence and

In Section 3.1 we introduce Lebesgue equivalence and define the complex vector space in Section 3.2 we define complex scalar products in 

Perhaps the reader has noticed some caginess in the introductory paragraph of this chapter. Why did we not say simply that the Hilbert space is 

We make tliis idea precise by defining an equivalence relation (see Sec- 

We will need only one special case of Fubini s theorem. 

Theorem 3.1 (Fubini s Theorem) Suppose f is a measurable complex-valued function of three variables. Suppose further that 

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