GEOMETRY AND PROBABILITY.

The present paper is chiefly based on the report delivered by the author on March 16, 2016 at the Principle Seminar of the Department of Probability held at the Faculty of Mechanics and Mathematics of Moscow State University. We describe in general terms the relations of the theory of probability with integral geometry and with the phenomenon of measure concentration in multidimensional geometry. In this context, we also discuss one general observation by A. N. Kolmogorov about the Gauss normal distribution, which was brought to the author's attention by A. N. Shiryaev. [ABSTRACT FROM AUTHOR]