9 citations · 18 across the 5 of their papers we have counts for
5 papers
Limit spectral measures of matrix distributions of metric triples
A. Vershik, F. Petrov
A notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is determin…
Virtual Continuity of Measurable Functions and Its Applications
A. Vershik, F. Petrov, P. Zatitskiy
Classical theorem of Luzin states that a measurable function of one real variable is "almost" continuous. For measurable functions of several variables the analogous statement (con…
Geometry and Dynamics of Admissible Metrics in Measure Spaces
A. Vershik, F. Petrov, P. Zatitskiy
We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a spe…
Correction of metrics
F. V. Petrov, P. B. Zatitskiy
We prove that a symmetric nonnegative function of two variables on a Lebesgue space that satisfies the triangle inequality for almost all triples of points is equivalent to some se…
Linearly rigid metric spaces and the embedding problem
J. Melleray, F. V. Petrov, A. M. Vershik
We consider the problem of isometric embedding of metric spaces to the Banach spaces; and introduce and study the remarkable class of so-called linearly rigid metric spaces: these…