Concentration of Product Spaces

Abstract

We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. We obtain a complete answer for this question.

Keywords

• metric measure space
• concentration topology
• box topology
• product space
• metric preserving function
• primary: 53c23
• secondary: 54e35, 26b35