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144 Chapter 7
The LP Spaces: Completeness and Approximation
14. Show that if f (x ) = In( 1/x) for x e (0, 1], then f belongs to LP(0, 1] for all 1 lt; p lt; oo but
does not belong to Lo ( 0, 1].
15. Formulate and prove an extension of Holder’s Inequality for the product of three functions
16. Suppose that ( f. I is bounded in /
110 11 Is If
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