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Preface | ||
1 | Introduction: Donsker's Theorem, Metric Entropy, and Inequalities | 1 |
2 | Gaussian Measures and Processes; Sample Continuity | 23 |
3 | Foundations of Uniform Central Limit Theorems: Donsker Classes | 91 |
4 | Vapnik-Cervonenkis Combinatorics | 134 |
5 | Measurability | 170 |
6 | Limit Theorems for Vapnik-Cervonenkis and Related Classes | 196 |
7 | Metric Entropy, with Inclusion and Bracketing | 234 |
8 | Approximation of Functions and Sets | 250 |
9 | Sums in General Banach Spaces and Invariance Principles | 285 |
10 | Universal and Uniform Central Limit Theorems | 314 |
11 | The Two-Sample Case, the Bootstrap, and Confidence Sets | 332 |
12 | Classes of Sets or Functions Too Large for Central Limit Theorems | 363 |
App. A | Differentiating under an Integral Sign | 391 |
App. B | Multinomial Distributions | 399 |
App. C | Measures on Nonseparable Metric Spaces | 402 |
App. D | An Extension of Lusin's Theorem | 405 |
App. E | Bochner and Pettis Integrals | 407 |
App. F | Nonexistence of Types of Linear Forms on Some Spaces | 413 |
App. G | Separation of Analytic Sets; Borel Injections | 417 |
App. H | Young-Orlicz Spaces | 421 |
App. I | Modifications and Versions of Isonormal Processes | 425 |
Subject Index | 427 | |
Author Index | 432 | |
Index of Notation | 435 |
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