A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions

英文摘要：

We prove that if a triplet of functions satisfies almost equality in the Prékopa-Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative stability estimate with computable constants.