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Ind-additive functionals on random vectors

Seria
Rozprawy Matematyczne tom/nr w serii: 72 wydano: 1970
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Warianty tytułu
Abstrakty
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CONTENTS
1. Introduction.......................................................................................................................................................................... 5
2. Preliminaries....................................................................................................................................................................... 6
3. Random vector measures................................................................................................................................................ 9
4. Random integrals of operator-valued functions........................................................................................................... 14
5. Ind-additive functionals...................................................................................................................................................... 21
6. A description of operator-valued functions that are integrable with respect
to the homogeneous random vector measure.................................................................................................................. 22
7. Vector lattices and additive functionals........................................................................................................................... 26
8. Representation of additive functionals on finite-dimensional vector lattices
and on F-lattices of typo M..................................................................................................................................................... 28
9. Representation of additive functionals on Orlicz spaces and $L_p$-type lattices
having a Freudenthal unit...................................................................................................................................................... 30
10. Representation of ind-additive functionals on non-Gaussian vectors................................................................... 35
References............................................................................................................................................................................... 37
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 72
Liczba stron
40
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXXII
Daty
wydano
1970
Twórcy
Bibliografia
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  • [6] Bretagnolle, J.-P. et Dacunha-Castelle, D., Measures aléatoires et espaces d'Orlicz, Comptes Rendus, Paris 264 (1967), p. 877-880.
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  • [8] Bretagnolle, J.-P., Dacunha-Castelle, D. et Krivine, J.-L., Lois stables et espaces $L^p$, Annales de l'Institut Henri Poincaré, Section B 2 (1966), p. 231-259.
  • [9] Chacon, R. V. and Friedman, N., Additive functionals, Archive for Rational Mechanics and Analysis 18 (1965), p. 230-240.
  • [10] Day, M. M., The spaces $L^p$ with 0 < p < 1, Bull. Amer. Math. Soc. 46 (1940), p. 816-823.
  • [11] Dunford, N. and Schwartz, J. T., Linear operators, Part I, Now York 1958.
  • [12] Friedman, N. and Katz, M., A representation theorem for additive functionals, Archive for Rational Mechanics and Analysis 21 (1966), p. 49-57.
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  • [15 Halmos, P. R., Measure theory, Princeton 1960.
  • [16] Kakutani, S., Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Ann. of Math. 42 (1941), p. 523-537.
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  • [18] Kingman, J. F. C., Completely random measures, Pacific J. of Math. 21 (1967), p. 59-78.
  • [19] Koshi, S., On additive functionals of measurable function spaoes, Math. J. of Okayama Univ. 13 (1968), p. 119-127(3).
  • [20] Krasnoselskiĭ, M. A., Topological methods in the theory of non-linear integral equations, Moscow 1956 (in Russian).
  • [21] Krasnoselskĭ, M. A. and Rutickiĭ, Ya. B., Convex functions and Orlicz spaces, Gröningen 1961.
  • [22] Lévy, P., Théorie de l'addition de variables aléatoires, Paris 1954.
  • [23] Loève, M., Probability theory, Princeton 1965.
  • [24] Martin, A. D. and Mizel, V. J., A representation theorem for certain non-linear functionals, Archive for Rational Mechanics and Analysis 15 (1964), p. 353-367.
  • [25] Matuszewska, W., On generalized Orlicz spaces, Bull. Acad. Polon. Sci. 8 (1960), p. 349-353.
  • [26] Matuszewska, W. and Orlicz, W., A note on the theory of s-normed spaces of p-integrable functions, Studia Math. 21 (1961), p. 117-133.
  • [27] Mazur, S. et Orlicz, W., Sur les espaces métriques linéaires I, ibidem 10 (1948), p. 184-208.
  • [28] Mizel, V. J., Representation of non-linear transformations and functionals on $L^p$-spaces, Report 68-16, Department of Math., Carnegie-Mellon University (3).
  • [29] Musielak, J. and Orlicz, W., On modular spaces, Studia Math. 18 (1959), p. 49-85.
  • [30] Prékopa, A., On stochastic set functions I, Acta Math. Acad. Sci. Hungaricac 7 (1956), p. 215-263.
  • [31] Prékopa, A., On stochastic set functions II, ibidem 8 (1957), p. 337-374.
  • [32] Prékopa, A., On stochastic set functions III, ibidem 8 (1957), p. 375-400.
  • [33] Rao, M. M., Linear functionals on Orlicz spaces, Nieuw Archief voor Wiskunde, 12 (1964), p. 77-98.
  • [34] Rao, M. M., Conditional expectations and closed projections, Indag. Math. 27 (1965), p. 100-112.
  • [35] Rao, M. M., Notes on pointwise convergence of closed martingales, ibidem 29 (1967), p. 170-176.
  • [36] Rao, M. M., Local functionals and generalised random fields, Bull. Amer. Math. Soc. 74 (1968), p. 288-293 (4).
  • [37] Skorokhod, A. W., Stochastic processes with independent increments, Moscow 1964 (in. Russian).
  • [38] Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 55 (1937), p. 375-481.
  • [39] Urbanik, K., Some prediction problems for strictly stationary processes, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. II, Part 1 (1967), p. 235-258.
  • [40] Urbanik, K., Random measures and harmonizable sequences, Studia Math. 31 (1968), p. 61-88.
  • [41] Urbanik, K. and Woyczyński, W. A., A random integral and Orlicz spaces, Bull. Acad. Polon. Sci. 15 (1967), p. 161-169.
  • [42] Woyczynski, W. A., Additive functionals on Orlicz spaces, Coll. Math. 10 (1968), p. 319-326.
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  • [44] Yosida, K., Functional analysis, Berlin-Göttingen-Heidelberg 1965.
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