The L p space of functions on a measure space (S, S,λ) was discussed in Section VI. 14. The special case p = 2 plays a strong role in analysis and will now be discussed in more detail in an abstract form. It is useful to allow complex valued measurable functions in this study. Complex conjugates are indicated by upper bars. Recall that a complex valued function f is measurable if and only if its real part ℜf and imaginary part ℑf are.
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