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

2008/03/21 by Kei Funano, Funano, Kei
Mathematics · #53C21 #53C23 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #math.FA #math.MG #msc:53C21 #msc:53C23

paper · pdf · doi:10.48550/arxiv.0803.3122

11pages

arxiv created 2008/03/21 · arxiv updated 2009/12/01

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 L¹ and L²-concentration of the maps.

Related

• Fubini-Tonelli type theorem for non product measures in a product space
• On Fubini type theorems for the Riemann integral
• A consistent Fubini-Tonelli theorem for nonmeasurable functions
• Observable concentration of mm-spaces into spaces with doubling measures
• On the regular convergence of multiple series of numbers and multiple integrals of locally integrable functions over \R^m₊