Random linear functionals
HTML articles powered by AMS MathViewer
- by R. M. Dudley
- Trans. Amer. Math. Soc. 136 (1969), 1-24
- DOI: https://doi.org/10.1090/S0002-9947-1969-0264726-2
- PDF | Request permission
References
- Salah Ahmad, Éléments aléatoires dans les espaces vectoriels topologiques, Ann. Inst. H. Poincaré Sect. B (N.S.) 2 (1965/1966), 95–135 (French). MR 0196773 S. Banach, Théorie des opérations linéaires, PWN, Warsaw, 1932; reprint, Chelsea, New York, 1955. N. Bourbaki, Espaces vectoriels topologiques, Hermann, Paris, 1955, Chapters III-V.
- Pierre Cartier, Processus aléatoires généralisés, Séminaire Bourbaki, 16e année: 1963/64, Fasc. 3, Secrétariat mathématique, Paris, 1964, pp. Exposé 272, 10 (French). MR 0175170
- R. M. Dudley, On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483–507. MR 175081, DOI 10.1090/S0002-9947-1964-0175081-6
- R. M. Dudley, Singular translates of measures on linear spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 128–137 (1964). MR 169277, DOI 10.1007/BF00535972
- R. M. Dudley, Singularity of measures on linear spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 6 (1966), 129–132. MR 210860, DOI 10.1007/BF00537135
- R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis 1 (1967), 290–330. MR 0220340, DOI 10.1016/0022-1236(67)90017-1
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606 N. Dunford and J. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
- J. Feldman, Extending complex quasi-measures, Teor. Verojatnost. i Primenen. 10 (1965), 375–379 (English, with Russian summary). MR 0222237
- I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 1, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1964 [1977]. Properties and operations; Translated from the Russian by Eugene Saletan. MR 0435831
- R. K. Getoor, On characteristic functions of Banach space valued random variables, Pacific J. Math. 7 (1957), 885–896. MR 88817
- Leonard Gross, Harmonic analysis on Hilbert space, Mem. Amer. Math. Soc. 46 (1963), ii+62. MR 161095
- Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der mathematischen Wissenschaften, Band 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156915 A. N. Kolmogorov, A note to the papers of R. A. Minlos and V. Sazonov, Teor. Verojatnost. i Primenen. 4 (1959), 237-239 = Theor. Probability Appl. 4 (1959), 221-223.
- Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342
- R. A. Minlos, Generalized random processes and their extension in measure, Trudy Moskov. Mat. Obšč. 8 (1959), 497–518 (Russian). MR 0108851
- Frigyes Riesz and Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR 0071727
- V. Sazonov, On characteristic functionals, Teor. Veroyatnost. i Primenen. 3 (1958), 201–205 (Russian, with English summary). MR 0098423
- I. E. Segal, Abstract probability spaces and a theorem of Kolmogoroff, Amer. J. Math. 76 (1954), 721–732. MR 63602, DOI 10.2307/2372714 V. N. Sudakov and A. M. Veršik, Topological questions in the theory of measures in linear spaces, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 217-219. (Russian)
- V. S. Varadarajan, Measures on topological spaces, Mat. Sb. (N.S.) 55 (97) (1961), 35–100 (Russian). MR 0148838
- Salomon Bochner, Harmonic analysis and the theory of probability, University of California Press, Berkeley-Los Angeles, Calif., 1955. MR 0072370
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 136 (1969), 1-24
- MSC: Primary 60.40
- DOI: https://doi.org/10.1090/S0002-9947-1969-0264726-2
- MathSciNet review: 0264726