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The Brunn-Miknowski inequality gives a lower bound on the Lebesgue measure of a sumset in terms of the measures of the individual sets. This classical inequality in convex geometry was inspired by issues around the isoperimetric problem and was considered for a long time to belong to geometry, where its significance is widely recognized. However, it is by now clear that the Brunn-Miknowski inequality has also applications in analysis, statistics, informations theory, etc. (we refer the reader to [29] for an extended exposition on the Brunn-Minkowski inequality and its relation to several other famous inequalities).KeywordsStability ResultIsoperimetric InequalityMinkowski InequalityIsoperimetric ProblemFast Diffusion EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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The Brunn-Miknowski inequality gives a lower bound on the Lebesgue measure of a sumset in terms of the measures of the individual sets. This classical inequality in convex geometry was inspired by issues around the isoperimetric problem and was considered for a long time to belong to geometry, where its significance is widely recognized. However, it is by now clear that the Brunn-Miknowski inequality has also applications in analysis, statistics, informations theory, etc. (we refer the reader to [29] for an extended exposition on the Brunn-Minkowski inequality and its relation to several other famous inequalities).KeywordsStability ResultIsoperimetric InequalityMinkowski InequalityIsoperimetric ProblemFast Diffusion EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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