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I'm so excited in log-concave and log-convex functions .

I find a good properties of that :

1- The Laplace transform of a non-negative function is a log-convex.
2- The convolution of two log -concave functions is log-concave.
3- The product of log-concave functions is log concave.

but I can't find any information about usefulness of these for any applications.

Thanks in advance .

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