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- W2000373554 abstract "If $f,g:mathbb{R}^nlongrightarrowmathbb{R}_{geq0}$ are non-negative measurable functions, then the Prekopa-Leindler inequality asserts that the integral of the Asplund sum (provided that it is measurable) is greater or equal than the $0$-mean of the integrals of $f$ and $g$. In this paper we prove that under the sole assumption that $f$ and $g$ have a common projection onto a hyperplane, the Prekopa-Leindler inequality admits a linear refinement. Moreover, the same inequality can be obtained when assuming that both projections (not necessarily equal as functions) have the same integral. An analogous approach may be also carried out for the so-called Borell-Brascamp-Lieb inequality." @default.
- W2000373554 created "2016-06-24" @default.
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- W2000373554 date "2015-03-28" @default.
- W2000373554 modified "2023-09-27" @default.
- W2000373554 title "On a linear refinement of the Pr'ekopa-Leindler inequality" @default.
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