Suppose that is a real number with . Let . Then we have that . For any positive and , the following inequality holds:

**Proof**: Note that and . Taking the log xy we have

If we then exponentiate, we have .

A measure theory book of mine (Measure, Integral and Probability, by Capinski) gives another proof, but I like this one, from PlanetMath, more.

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Hi! Interesting blog. I do have a suggestion, WordPress can parse latex code 🙂

Comment by chuckie — July 15, 2008 @ 7:26 am |