Bochner property in Banach spaces
Naik-Nimbalkar, Uttara
Annales de l'I.H.P. Probabilités et statistiques, Tome 17 (1981), p. 1-19 / Harvested from Numdam
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Publié le : 1981-01-01
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     author = {Naik-Nimbalkar, Uttara},
     title = {Bochner property in Banach spaces},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {17},
     year = {1981},
     pages = {1-19},
     mrnumber = {610495},
     zbl = {0459.60001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1981__17_1_1_0}
}

Naik-Nimbalkar, Uttara. Bochner property in Banach spaces. Annales de l'I.H.P. Probabilités et statistiques, Tome 17 (1981) pp. 1-19. http://gdmltest.u-ga.fr/item/AIHPB_1981__17_1_1_0/

[1] A. De Acosta, Existence and convergence of probability measures in Banach . spaces, Trans. Amer. Math. Soc., t. 152, 1970, p. 273-298. | MR 267614 | Zbl 0226.60007

[2] A. De Acosta, Banach spaces of stable type and the generation of stable measures, prepint, 1975.

[3] A. Badrikian, Séminaire sur les fonctions aléatoires linéaires et les measures cylindriques, Lecture Notes in Math. (Springer-Verlag), t. 139, 1970. | MR 279271 | Zbl 0209.48402

[4] P. Billingsley, Convergence of probability measures, Wiley, New York, MR, t. 38, p. 1718. | MR 1700749 | Zbl 0172.21201

[5] L. Breiman, Probability, Addison-Wesley, Reading, 1968. | MR 229267 | Zbl 0174.48801

[6] N. Dunford and J.T. Schwartz, Linear operators, Interscience, New York, t. 1, 1957. | Zbl 0084.10402

[7] W. Feller, An introduction to probability theory and its applications, Vol. II, John Wiley and Sons, New York, 1966. | MR 210154 | Zbl 0138.10207

[8] X. Fernique, Integrabilite des vecteurs Gaussien, G. R. Acad. Sc. Paris, Sene A. t. 270, 1971, p. 1698-1699. | MR 266263 | Zbl 0206.19002

[9] D.J.H. Garling, Functional central limit theorem in Banach spaces, Ann. Prob., t. 4, 1976, p. 600-611. | MR 423449 | Zbl 0343.60014

[10] L. Gross, Harmonic analysis on Hilbert spaces, Mem. Amer. Math. Soc., t. 46, 1963. | MR 161095 | Zbl 0118.32201

[11] P. Halmos, Measure theory, Princeton, 1950. | MR 33869 | Zbl 0040.16802

[12] K. Ito and M. Nisio, Sums of independent Banach space valued random variables. Osaka, J. Math., t. 5, 1968, p. 35-48. | MR 235593 | Zbl 0177.45102

[13] J. Kuelbs, Fourier Analysis on linear metric spaces, Trans. Amer. Math. Soc., t. 181, 1973, p. 293-311. | MR 331455 | Zbl 0291.60001

[14] S. Kwapien, Isomorphic characterizations of inner-product spaces by orthogonal series with vector valued coefficients, Studia Math., t. 44, 1972, p. 583-595. | MR 341039 | Zbl 0256.46024

[15] J. Lindenstrauss and A. Pelczynski, Absolutely summing operators in Lp-spaces and their applications, Studia Math., t. 29, 1968, p. 275-326. | MR 231188 | Zbl 0183.40501

[16] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., t. 338, 1973, Springer-Verlag, New York. | MR 415253 | Zbl 0259.46011

[17] M. Loeve, Probability theory, 3rd Ed., Van Nostrand, Princeton, 1963. | MR 203748 | Zbl 0108.14202

[18] V. Mandrekar, On Bochner and Levy theorems in Orlicz spaces, Symp. Math., t. 21, 1977, p. 177-186. | MR 482904 | Zbl 0372.46033

[19] V. Mandreakar, Characterization of Banach space through validity of Bochner Theorem, Lecture Notes in Math., t. 644, 1977, Springer-Verlag. | Zbl 0498.60010

[20] B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp, Société Mathématique de France, Astérique, t. 11, 1974, p. 1-163. | MR 344931 | Zbl 0278.46028

[21] B. Maurey and G. Pisier, Series de variables aleatones vectorielles independentes et proprietes geometriques des espaces de Banach, Studia Math., t. 58, 1976, p. 45-90. | MR 443015 | Zbl 0344.47014

[22] D.K.H. Mustari, Certain general questions in the theory of probability measures in linear spaces, Theor. Prob. Appl. (S. I. A. M. translations), t. 18, 1973, p. 64-75. | Zbl 0304.60003

[23] D.K.H. Mustari, On a probabilistic characterization of Hilbert space, Theor. Prob. Appl. (S. I. A. M. translation), t. 21, 1976, p. 410-412. | MR 418178 | Zbl 0358.60008

[24] K.R. Parthasarathy, Propability measures on metric spaces, Academic Press, New York, 1967. | MR 226684 | Zbl 0153.19101

[25] V. Yu Prohorov, Convergence of random processes and limit theorems in probability theory, Theor. Prob. Appl. (S. I. A. M. translation), t. 1, 1956, p. 157-214. | MR 84896 | Zbl 0075.29001

[26] H. Rosenthal, The Banach spaces C(K) and Lp(μ). Bull. Amer. Math. Soc., t. 81, no. 5, 1975, p. 763-781. | MR 380381 | Zbl 0334.46033

[27] H. Sato, Hilbertian support of probability measures on a Banach space, Lecture Notes in Math., t. 709, Springer Verlag. | Zbl 0398.60006

[28] V. Sazanov, On characteristic functionals, Theor. Prob. Appl. (S. I. A. M. translation), t. 3, 1958, p. 189-193. | Zbl 0089.33801

[29] Michael Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist., t. 41, 1970, 412-421. | MR 254915 | Zbl 0196.19401

[30] A. Tortrat, Sur les lois e(λ) dans les espaces vectoriels, Applications aux lois stables, preprint, Lab. de Prob., Univ. of Paris, 1975.

[31] B. Maurey, Un théorème de prolongement, C. R. A. S., t. 279, 1974, p. 329-332. | MR 355539 | Zbl 0291.47001