Donsker classes of sets

DOI10.1007/BF00322017zbMath0628.60027MaRDI QIDQ1093240

Michel Talagrand

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

rate of convergencelaw of large numbersempirical processescentral limit theoremlocal theory of Banach spaces

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Measures and integrals in product spaces (28A35)

Related Items

Vapnik-Chervonenkis dimension and (pseudo-)hyperplane arrangements, Sphere packing numbers for subsets of the Boolean \(n\)-cube with bounded Vapnik-Chervonenkis dimension, Gelfand numbers of operators with values in a Hilbert space, VC bounds on the cardinality of nearly orthogonal function classes, A CLT for empirical processes involving time-dependent data, The Glivenko-Cantelli problem, ten years later, Selector processes on classes of sets, Gaussian approximation of the empirical process under random entropy conditions, A note on limit theorems for perturbed empirical processes, Komlós-Major-Tusnády approximation for the general empirical process and Haar expansions of classes of functions

Cites Work

• Regularity of Gaussian processes
• Embedding of \(\ell^ k_{\infty}\) in finite dimensional Banach spaces
• Some limit theorems for empirical processes (with discussion)
• Measurability problems for empirical processes
• The Glivenko-Cantelli problem
• Donsker classes and random geometry
• The central limit theorem for stochastic processes. II
• Empirical discrepancies and subadditive processes
• The dimension of almost spherical sections of convex bodies
• On the density of families of sets
• Pettis integral and measure theory