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

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.