Let $(X, \mathscr{A}, P)$ be a probability space. Let $X_1, X_2,\cdots,$ be independent $X$-valued random variables with distribution $P$. Let $P_n := n^{-1}(\delta_{X_1} + \cdots + \delta_{X_n})$ be… Expand

The first two sections of this paper are introductory and correspond to the two halves of the title. As is well known, there is no complete analog of Lebesue or Haar measure in an… Expand

This is a survey on sample function properties of Gaussian processes with the main emphasis on boundedness and continuity, including Holder conditions locally and globally. Many other sample function… Expand

Let (S, d) be a separable metric space. Let \( P; > \left( S \right)\) be the set of Borel probability measures on S. \(C\left( S \right)\) denotes the Banach space of bounded continuous real-valued… Expand

Let I(k, α, M) be the class of all subsets A of R k whose boundaries are given by functions from the sphere S k −1 into R k with derivatives of order % α, all bounded by M. (The precise definition,… Expand

When \(\mathfrak{F}\) is a universal Donsker class, then for independent, indetically distributed (i.i.d) observation \(\mathbf{X}_1,\ldots,\mathbf{X}_n\) with an unknown law P, for any… Expand