The majorizing measure approach to the sample boundedness

Abstract: In this paper we describe the alternative approach to the sample boundedness and continuity of stochastic processes. We show that the regularity of paths can be understood in terms of a distribution of the argument maximum. For a centered Gaussian process X(t), t\in T we obtain a short proof of the exact lower bound on E\sup_{t\in T} X(t). Finally we prove the equivalence of a usual majorizing measure functional to its conjugate version.