The $mm$-space (or admissible triple, or Gromov triple) is a metric space with probability measure with

some (very weak) condition on concordance between two structures.

The point of view of author is: to fix measure structure and to vary the metrics as the measurable functions

of two variables.

Then the space of continuous measure spaces is the cone of the metrics on the standard measure space

(Lebesgue space). The series of natural properties of the triples will be formulated in the talk.

The main fact (Gromov,Vershik) is the theorem about classification of the mm-spaces up to measure preserving

isometries. The complete invariant of $mm$-spaces is so called matrix distributions --- the measure on the matrices

of distances or random matrices. Analysis of $mm$-spaces is the theory of matrix distributions.

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Speaker:

Anatoly Vershik
Affiliation:

St. Petersburg Department of Steklov Institute of Mathematics
Date:

Fri, 2017-09-15 09:30 - 10:30
Location:

MPIM Lecture Hall
Parent event:

Metric Measure Spaces and Ricci Curvature