Author | Vakhania, N. N. author |
---|---|
Title | Probability Distributions on Banach Spaces [electronic resource] / by N. N. Vakhania, V. I. Tarieladze, S. A. Chobanyan |
Imprint | Dordrecht : Springer Netherlands, 1987 |
Connect to | http://dx.doi.org/10.1007/978-94-009-3873-1 |
Descript | XXVI, 482 p. online resource |
I. Measurability and Measures -- 1. ?-algebras and measurable mappings in metric space -- 2. ?-algebras in Banach spaces -- 3. Probability measures on topological spaces -- 4. The semigroup of probability measures -- 5. Invariant and quasi-invariant measures. Scalarly non-degenerate measures -- Supplementary comments -- II. Measures and Random Elements. Weak and Strong Orders -- 1. Random elements -- 2. Weak and strong orders of random elements -- 3. The expectation -- 4. Conditional expectations, martingales and connections with the Radon-Nikodym Property -- Supplementary comments -- III. Covariance Operators -- 1. Operators mapping spaces into their duals -- 2. Covariance operators -- Supplementary comments -- IV. Characteristic Functionals -- 1. Positive-definite functions -- 2. Definition and general properties of characteristic functionals -- 3. Characteristic functionals and weak convergence -- 4. Bochnerโs theorem -- Supplementary comments -- V. Sums of Independent Random Elements -- 1. Independent random elements -- 2. Series of independent random elements -- 3. Integrability of sums and the mean convergence of random series -- 4. Comparison of random series -- 5. Some special series -- 6. Random series in spaces which do not contain c0 -- Supplementary comments -- VI. Topological Description of Characteristic Functionals and Cylindrical Measures -- 1. Sazonovโs theorem and related topics -- 2. Necessary and sufficient topologies. Spaces with the Sazonov property -- 3. Cylindrical measures -- 4. The case of locally convex spaces. Minlosโ theorem -- 5. Radonifying operators -- Supplementary comments