On a construction of majorizing measures on subsets of $\mathbb R^n$ with special metrics

Volume 197 / 2010

Jakub Olejnik Studia Mathematica 197 (2010), 1-12 MSC: Primary 60G07, 40A30, 60G17; Secondary 28A99. DOI: 10.4064/sm197-1-1

Abstract

We consider processes $X_t$ with values in $L_p({\mit\Omega},\mathcal{F},P)$ and “time” index $t$ in a subset $A$ of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains $A$ for which all such processes are a.e. continuous. We use the notion of Talagrand's majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set $A$. A majorizing measure is constructed.

Authors

  • Jakub OlejnikFaculty of Mathematics and Computer Science
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland
    e-mail

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