An asymptotic variant of the Fubini theorem for maps into CAT(0)-spaces

TL;DR

This paper develops an asymptotic version of the Fubini theorem applicable to maps into CAT(0)-spaces, based on concentration phenomena in L^1 and L^2 spaces, extending classical integral interchange results.

Contribution

It introduces an asymptotic Fubini theorem for CAT(0)-space-valued maps using concentration of measure, a novel extension of classical integral interchange principles.

Findings

Derived an asymptotic Fubini theorem for CAT(0)-spaces

Utilized L^1 and L^2 concentration properties

Extended classical integral interchange results to metric space maps

Abstract

The classical Fubini theorem asserts that the multiple integral is equal to the repeated one for any integrable function on a product measure space. In this paper, we derive an asymptotic variant of the Fubini theorem for maps into CAT$(0)$-spaces from the $L^1$ and $L^2$-concentration of the maps.