L^p-norm inequality using q-moment and its applications

02/04/2019

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by   Tomohiro Nishiyama, et al.

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For a measurable function on a set which has a finite measure, an inequality holds between two Lp-norms. In this paper, we show similar inequalities for the Euclidean space and the Lebesgue measure by using the q-moment. As applications of these inequalities, we first derive inequalities for the Renyi and the Tsallis entropy. Second, we derive an inequality between a probability of a subset in the Euclidean space and the Lp-norm on the same set.