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Cambridge Studies in Advanced Mathematics


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Table of Contents

1. Foundations: set theory; 2. General topology; 3. Measures; 4. Integration; 5. Lp spaces: introduction to functional analysis; 6. Convex sets and duality of normed spaces; 7. Measure, topology, and differentiation; 8. Introduction to probability theory; 9. Convergence of laws and central limit theorems; 10. Conditional expectations and martingales; 11. Convergence of laws on separable metric spaces; 12. Stochastic processes; 13. Measurability: Borel isomorphism and analytic sets; Appendixes: A. Axiomatic set theory; B. Complex numbers, vector spaces, and Taylor's theorem with remainder; C. The problem of measure; D. Rearranging sums of nonnegative terms; E. Pathologies of compact nonmetric spaces; Indices.

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This classic text offers a clear exposition of modern probability theory.


'A marvellous work which will soon become a standard text in the field for both teaching and reference ... a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs throughout the text. Some of the topics and proofs are rarely found in other textbooks.' Proceedings of the Edinburgh Mathematical Society 'Careful, scholarly, and stimulating. It would be a pleasure to teach a mathematically-oriented graduate-level course from this text.' Short Book Reviews of the ISI '[It] will serve for a long time as a standard reference.' Zentralblatt fur und ihre Grenzgebiete 'What makes the book special ... is the care and scholarship with which the material is treated, and the choice of additional topics ... not usually covered in first year graduate courses.' Mathematical Reviews 'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields ... it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter

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