Uniform measures on the arbitrary compact metric spaces, with applications

Abstract

We introduce and investigate in this short report the new notion of uniform measure (distribution) on the arbitrary compact metric space. We consider also some possible applications of these measures in the theory of imbedding theorems and in the theory of random processes (fields), in particular, in the so-called majorizing (and minorizing) measures method, belonging to X.Fernique and M.Talagrand. These considerations based on the L.Arnold and P.Imkeller generalization of the classical A.M.Garsia-E.Rodemich-H.Jr.Rumsey inequality and X.Fernique-M.Talagrand estimation for random fields.