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

We prove that if a triplet of functions satisfies almost -equality in the Pr & eacute;kopa-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.