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Integration in Hilbert Space

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Author(s): A.V. Skorohod
Publisher: Springer
Year: 1974

Language: english

Cover
Title page
Prefaces
Introduction
Chapter 1. Definition of a Measure in Hilbert Space
1. Measurable Hilbert Spaces
2. Weak Distributions
3. The Charaeteristie Functional. Moment Functionals
4. The Minlos-Sazonov Theorem
5. Gaussian Measures
6. Generalized Measures in Hilbert Spaee
Chapter 2. Measurable Funetions on Hilbert Space
7. Measurable Linear Functionals
8. Measurable Linear Operators
9. Measurable Polynomial Funetions
10. Square-integrable Polynomials
11. Orthogonal Systems of Polynomials
12. Polynomials Orthogonal with Respect to a Weight Function
Chapter 3. Absolute Continuity of Measures
13. The Radon-Nikodym Theorem. Conditional Measures
14. Martingales and Semi-Martingales
15. General Conditions for Absolute Continuity
16. Absolute Continuity of Product Measures
17. Absolute Continuity of Gaussian Measures
18. Absolute Continuity of Mixed Measures
Chapter 4. Admissible Shifts and Quasi-invariant Measures
19. Admissible Shifts of Measures
20. Admissible Directions
21. Differentiation of Measures w.r.t. a Direction
22. An Admissibility Condition for Shifts
23. Quasi-invariant Measures
Chapter 5. Some Questions of Analysis in Hilbert Spaee
24. The Substitution Formula and Absolute Continuity
25. Linear Transformations
26. Absolute Continuity of Measures under Nonlinear Transformations
27. Surface Integrals
28. Gauss' Formula
Bibliographic Notes
Bibliography
Index