Uniform measures on the arbitrary compact metric spaces, with applications

2014/03/23 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1403.5725

openalex publication_date 2014/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Asymptotic exponential bounds for MLE deviation under minimal conditions via classical and generic chaining methods
• Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)
• A counterexample to a hypothesis of light tail of maximum distribution for continuous random processes with light finite-dimensional tails
• Module of continuity for the functions belonging to the Sobolev-Grand Lebesgue Spaces
• Hitchhiker's guide to the fractional Sobolev spaces

Cited by

• Sufficient conditions for exponential tightness of normed sums of independent random fields in the space of continuous functions

Related

• Simplification of the majorizing measures method, with development
• Point distributions in compact metric spaces, II
• Point distributions in compact metric spaces
• Unimodular Random Measured Metric Spaces and Palm Theory on Them
• Majorizing Measures, Codes, and Information