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This second edition of the classic work on empirical processes has been considerably expanded and revised, including several new proved theorems not included in the first edition.
List of contents
1. Donsker's theorem and inequalities; 2. Gaussian processes, sample continuity; 3. Definition of Donsker classes; 4. Vapnik-Cervonenkis combinatorics; 5. Measurability; 6. Limit theorems for VC-type classes; 7. Metric entropy with bracketing; 8. Approximation of functions and sets; 9. Two samples and the bootstrap; 10. Uniform and universal limit theorems; 11. Classes too large to be Donsker; Appendix A. Differentiating under an integral sign; Appendix B. Multinomial distributions; Appendix C. Measures on nonseparable metric spaces; Appendix D. An extension of Lusin's theorem; Appendix E. Bochner and Pettis integrals; Appendix F. Non-existence of some linear forms; Appendix G. Separation of analytic sets; Appendix H. Young-Orlicz spaces; Appendix I. Versions of isonormal processes.
About the author
R. M. Dudley is a Professor of Mathematics at the Massachusetts Institute of Technology in Cambridge, Massachusetts.
Summary
This second edition of a classic work has been considerably expanded and revised, now with complete proofs of all results, including several new theorems not included in the first edition, such as Talagrand's generic chaining approach to boundedness of Gaussian processes and Giné and Zinn's characterization of uniform Donsker classes.
