For almost fifty years, Richard M. Dudley has been extremely influential in the development of several areas of Probability. This book includes his major journal publications for the last fifty years as well as commentary by the editors.

Includes his major journal publications plus commentaries in the papers by the editors. Includes a complete bibliography Electronic version is freely available on SpringerLink

Zusammenfassung
As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm.

Inhalt
Convergence in Law.- Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces.- Measures on Non-Separable Metric Spaces.- Distances of Probability Measures and Random Variables.- An Extended Wichura Theorem, Definitions of Donsker Class, and Weighted Empirical Distributions.- Markov Processes.- Lorentz-invariant Markov processes in relativistic phase space.- A note on Lorentz-invariant Markov processes.- Asymptotics of Some Relativistic Markov Processes.- Gaussian Processes.- The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes.- On seminorms and probabilities, and abstract Wiener spaces.- Sample Functions of the Gaussian Process.- On the Lower Tail of Gaussian Seminorms.- Empirical Processes.- Special Invited Paper.- Empirical and Poisson Processes on Classes of Sets or Functions Too Large for Central Limit Theorems.- Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes.- Universal Donsker Classes and Metric Entropy.- Nonlinear functionals and p-variation.- Fréchet Differentiability, p-Variation and Uniform Donsker Classes.- The Order of the Remainder in Derivatives of Composition and Inverse Operators for p-Variation Norms.- Empirical Processes and p-variation.- Miscellanea.- Pathological Topologies and Random Walks on Abelian Groups.- Metric Entropy of Some Classes of Sets with Differentiable Boundaries.- Wiener Functionals as Itô Integrals.- A Metric Entropy Bound is Not Sufficient for Learnability.- Asymptotic Normality with Small Relative Errors of Posterior Probabilities of Half-Spaces.