Author | Skorohod, A. V. author |
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Title | Integration in Hilbert Space [electronic resource] / by A. V. Skorohod |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1974 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65632-3 |
Descript | XII, 180 p. online resource |
1. Definition of a Measure in Hubert Space -- ยง 1. Measurable Hubert Spaces -- ยง 2. Weak Distributions -- ยง 3. The Characteristic Functional. Moment Functional -- ยง 4. The Minlos-Sazonov Theorem -- ยง 5- Gaussian Measures -- ยง 6. Generalized Measures in Hubert Space -- 2. Measurable Functions on Hubert Space -- ยง 7. Measurable Linear Functional -- ยง 8. Measurable Linear Operators -- ยง 9. Measurable Polynomial Functions -- ยง 10. Square-integrable Polynomials -- ยง 11. Orthogonal Systems of Polynomials -- ยง 12. Polynomials Orthogonal with Respect to a Weight Function -- 3. Absolute Continuity of Measures -- ยง 13. The Radon-Nikodym Theorem. Conditional Measures -- ยง 14. Martingales and Semi-Martingales. -- ยง 15. General Conditions for Absolute Continuity -- ยง 16. Absolute Continuity of Product Measures -- ยง 17. Absolute Continuity of Gaussian Measures -- ยง 18. Absolute Continuity of Mixed Measures -- 4. Admissible Shifts and Quasi-invariant Measures -- ยง 19. Admissible Shifts of Measures -- ยง 20. Admissible Directions -- ยง 24. Differentiation of Measures w.r.t. a Direction -- ยง 22. An Admissibility Condition for Shifts -- ยง 23. Quasi-in variant Measures -- 5. Some Questions of Analysis in Hubert Space -- ยง 24. The Substitution Formula and Absolute Continuity -- ยง 25. Linear Transformations -- ยง 26. Absolute Continuity of Measures under Nonlinear Transformation -- ยง 27. Surface Integrals. -- ยง 28. Gauss'Formula -- Bibliographic Notes