High Dimensional Probability III (Progress in Probability)
Contributors: Joergen Hoffmann-Joergensen (Editor); Michael B. Marcus (Editor); Jon A. Wellner (Editor)
Edition: 1 edition
Publisher: Birkhauser
Published: January 22, 2004
Language: eng
Format: Hardcover
Number of pages: 346
ISBN-13: 9783764321871
Subjects: Probability & statistics; Science/Mathematics; Mathematics; Mathematical Analysis; Probability & Statistics - General; Deviations; Limit theorems; Mathematics / Mathematical Analysis; Measure theory; Probability theory; Stochastic processes; Probability & Statistics - Multivariate Analysis
First sentence: In the theory of empirical processes and uniform convergence of stochastic processes, non-measurable norms and non-measurable "random elements" occur naturally and a crucial part of the theory consists in extending the classical inequalities (Levy's inequality, Ottaviani's inequality, Jensen's inequality, the symmetrization inequalities, the exponential inequality and the subgaussian inequalities) to vector valued non-measurable functions under various independence and regularity conditions.