H�lder's Inequality
Revision as of 17:03, 11 July 2006 by ComplexZeta (talk | contribs)
Statement
If , , then and .
Proof
If then a.e. and there is nothing to prove. Case is similar. On the other hand, we may assume that for all . Let . Young's Inequality gives us
These functions are measurable, so by integrating we get