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1. Probability and measure theory [2000]
 Ash, Robert B.
 2nd ed.  San Diego : Harcourt/Academic Press, c2000.
 Description
 Book — xii, 516 p. : ill. ; 24 cm.
 Summary

 Summary of Notation Fundamentals of Measure and Integration Theory. Further Results in Measure and Integration Theory. Introduction to Functional Analysis. Basic Concepts of Probability. Conditional Probability and Expectation. Strong Laws of Large Numbers and Martingale Theory. The Central Limit Theorem. Ergodic Theory. Brownian Motion and Stochastic Integrals.
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QA273 .A78 2000  Unknown 
2. Real analysis and probability [1972]
 Ash, Robert B.
 New York, Academic Press [1972]
 Description
 Book — xv, 476 p. 24 cm.
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QA273 .A78 1972  Unknown 
QA273 .A78 1972  Unknown 
3. Probabilistic techniques in analysis [1995]
 Bass, Richard F.
 New York : SpringerVerlag, c1995.
 Description
 Book — xii, 392 p. : ill. ; 24 cm.
 Summary

In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning PhD student. Highlights include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz's theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that the reader has some background in basic real analysis, but the book includes proofs of all results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are discussions of open problems and further avenues of research.
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QA300 .B33 1995  Unknown 
4. Real analysis and probability [2002]
 Dudley, R. M. (Richard M.)
 Cambridge ; New York : Cambridge University Press, 2002.
 Description
 Book — x, 555 p. ; 24 cm.
 Summary

 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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QA300 .D83 2002  Unknown 
5. Real analysis and probability [1989]
 Dudley, R. M. (Richard M.)
 Pacific Grove, Calif. : Brooks/Cole Pub. Co., 1989.
 Description
 Book — xi, 436 p. : ill. ; 24 cm.
 Summary

 Foundations: set theory. General topology. Measures. Integration. Lp spaces: introduction to functional analysis. Convex sets and duality of normed spaces. Measure, topology and differentiation. Introduction to probability theory. Convergence of laws and central limit theorems. Conditional expectation and martingales. Convergence of laws on separable metric spaces. Stochastic processes. Measurability: Borel isomorphism and analytic sets. Appendices.
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QA300 .D83 1989  Unknown 
 Sakhnovich, L. A.
 Basel ; London : Birkhäuser, c2012.
 Description
 Book — ix, 245 p. ; 24 cm.
 Summary

 Introduction.
 1 Levy processes.
 2 The principle of imperceptibility of the boundary.
 3 Approximation of positive functions.
 4 Optimal prediction and matched filtering.
 5 Effective construction of a class of nonfactorable operators.
 6 Comparison of thermodynamic characteristics.
 7 Dual canonical systems and dual matrix string equations.
 8 Integrable operators and Canonical Differential Systems.
 9 The game between energy and entropy.
 10 Inhomogeneous Boltzmann equations.
 11 Operator Bezoutiant and concrete examples. Comments. Bibliography. Glossary. Index.
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QA274.73 .S25 2012  Unknown 
7. Lectures
 Symposium on Probability Methods in Analysis (1966 : Loutraki, Greece)
 Berlin, New York, SpringerVerlag, 1967.
 Description
 Book — 329 p. 28cm.
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Shelved by Series title V.31  Unknown 
 Wise, Gary L., 1945
 New York : Oxford University Press, 1993.
 Description
 Book — 211 p.
 Summary

Ideas in mathematical sciences that might seem intuitively obvious may be proved incorrect with the use of their counterexamples. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among treatments of counterexamples. The authors maintain that, in fact, if taught correctly, probability theory cannot be separated from real analysis.
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QA273 .W67 1993  Unknown 
 New Jersey : World Scientific, 2009.
 Description
 Book — x, 272 p. : ill. ; 24 cm.
 Summary

 Entropy and Martingale (K B Athreya & M G Nadkarni) Marginal Quantiles: Asymptotics for Functions of Order Statistics (J Babu) Statistics on Manifolds with Applications to Shape Spaces (R Bhattacharya & A Bhattacharya) Reinforcement Learning  A Bridge Between Numerical Methods and Monte Carlo (V S Borkar) Bayesian Nonparametric Approach to Multiple Testing (S Ghosal & A Roy) Higher Criticism in the Context of Unknown Distribution, NonIndependence and Classification (P Hall) Bayesian Inference on Mixtures of Distributions (K Lee et al.) Markov Processes Generated by Random Iterates of Monotone Maps: Theory and Applications (M Majumdar) An Invitation to Quantum Information Theory (K R Parthasarathy) On the Classification of Binary Shifts on the Hyperfinite II1 Factor (G L Price) Scaling Limit (S R S Varadhan).
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QA273 .P47 2009  Unknown 
 Berlin ; New York : SpringerVerlag, 1986.
 Description
 Book — viii, 283 p. ; 25 cm.
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Serials  
Shelved by Series title V.1206  Unknown 