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Martingales et derivation. (French) Zbl 0146.37601


References:

[1] BOCHNER (S.) . - Additive set functions on groups , Annals of Math., t. 40, 1939 , p. 769-799. MR 1,110e | Zbl 0024.04203 | JFM 65.1317.01 · Zbl 0024.04203 · doi:10.2307/1968893
[2] BOCHNER (S.) and PHILLIPS (R. S.) . - Additive set functions and vector lattices , Annals of Math., t. 42, 1941 , p. 316-324. MR 2,315d | Zbl 0026.00104 | JFM 67.0162.02 · Zbl 0026.00105 · doi:10.2307/1969000
[3] BOCHNER (S.) . - Partial ordering in the theory of martingales , Annals of Math., t. 62, 1955 , p. 162-169. MR 17,167c | Zbl 0068.11302 · Zbl 0068.11302 · doi:10.2307/2007106
[4] CARATHÉODORY (C.) . - Mass und Integral und ihre Algebraisierung . - Basel, Stuttgart, Birkhäuser Verlag, 1956 (Lehrbücher und Monographien..., Mathematische Reihe, 10). MR 18,117c | Zbl 0074.04003 · Zbl 0074.04003
[5] CESARI (L.) . - Surface area . - Princeton, Princeton University Press, 1956 (Annals of Mathematics Studies, 35). MR 17,596b | Zbl 0073.04101 · Zbl 0073.04101
[6] CESARI (L.) . - Area and measure . Brunswick, Summer Institute, 1958 .
[7] CHIANG (Tse-Pei) . - Une remarque sur la définition de la quantité d’information [en russe] , Teorija Veroj. Prim., t. 3, 1958 , p. 99-103. Zbl 0080.12103 · Zbl 0080.12103
[8] CHOW (Y. S.) . - Martingales in a \sigma -finite measure space indexed by directed sets , Trans. Amer. math. Soc., t. 97, 1960 , p. 254-285. MR 22 #12565 | Zbl 0102.13402 · Zbl 0102.13402 · doi:10.2307/1993302
[9] COTLAR (M.) y FRENKEL (Y.) . - Una teoria general de integral basada en una extensión del concepto de limite , Univ. nac. Tucuman, Rivista, Série A, t. 6, 1947 , p. 113-159. MR 10,107a | Zbl 0032.19602 · Zbl 0032.19602
[10] DIEUDONNÉ (J.) . - Sur un théorème de Jessen , Fund. Math., t. 37, 1950 , p. 242-248. Article | MR 13,218d | Zbl 0040.01902 · Zbl 0040.01902
[11] DOOB (J. L.) . - Stochastic processes . - New York, J. Wiley ; London, Chapman and Hall, 1953 (Wiley Publications in Statistics). MR 15,445b | Zbl 0053.26802 · Zbl 0053.26802
[12] DOOB (J. L.) . - Semimartingales and subharmonic functions , Trans. Amer. math. Soc., t. 77, 1954 , p. 86-121. MR 16,269a | Zbl 0059.12205 · Zbl 0059.12205 · doi:10.2307/1990680
[13] DOOB (J. L.) . - Notes on martingale theory , Proceedings of the Fourth Berkeley symposium on mathematical statistics and probability [4, 1960 , Berkeley] ; vol. 2, p. 95-102. - Berkeley, Los Angeles, University of California Press, 1961 . Zbl 0126.14003 · Zbl 0126.14003
[14] DUBROVSKIJ (V. M.) . - Sur la base d’une famille de fonctions d’ensemble complètement additives et sur les propriétés d’additivité uniforme et d’équicontinuité [en russe] , Doklady Akad. Nauk S. S. S. R., N. S., t. 58, 1947 , p. 737-740. Zbl 0029.11503 · Zbl 0029.11503
[15] DUNFORD (N.D.) and TAMARKIN (J. D.) . - A principle of Jessen and general Fubini theorems , Duke math. J., t. 8, 1941 , p. 743-749. Article | MR 3,207a | Zbl 0061.25003 · Zbl 0061.25003 · doi:10.1215/S0012-7094-41-00863-3
[16] FUGLEDE (B.) . - On a theorem of F. Riesz , Math. Scand., t. 3, 1955 , p. 283-302. MR 18,198b | Zbl 0067.27901 · Zbl 0067.27901
[17] GOFFMAN (C.) and WATERMAN (D.) . - On upper and lower limits in measure , Notices Amer, math. Soc., t. 5, 1958 , p. 812. · Zbl 0113.04005
[18] HAHN (H.) and ROSENTHAL (A.) . - Set functions . - Albuquerque, N. M., University of New Mexico Press, 1948 . MR 9,504e | Zbl 0033.05301 · Zbl 0033.05301
[19] HALMOS (P. R.) . - Measure thoery . - Toronto, New York, London, Van Nostrand Company, 1950 (The University Series in higher Mathematics). · Zbl 0040.16802
[20] HAUPT (O.) , AUMANN (G.) und PAUC (C.) . - Differential- und Integralrechnung , III, 2te Auflage. - Berlin, W. de Gruyter, 1955 (Göschens lehrbücherei, Reine und angewandte Mathematik, 26). Zbl 0064.04801 · Zbl 0064.04801
[21] HAUPT (O.) et PAUC (C.) . - Propriétés de mesurabilité de bases de dérivation , Portugalià\? Math., t. 13, 1954 , p. 37-54. Article | MR 16,805a | Zbl 0056.27601 · Zbl 0056.27601
[22] HAYES (C. A. Jr) and PAUC (C.) . - Full individual and class differentiation theorems in their relations to halo and Vitali properties , Canad. J. Math., t. 7, 1955 ,p. 221-274. MR 17,719a | Zbl 0068.04602 · Zbl 0068.04602 · doi:10.4153/CJM-1955-028-9
[23] HELMS (L. L.) . - Mean convergence of martingales , Trans. Amer. math. Soc., t. 87, 1958 , p. 439-446. MR 20 #1350 | Zbl 0080.11904 · Zbl 0080.11904 · doi:10.2307/1993109
[24] JERISON (M.) and RABSON (G.) . - Convergence theorems obtained from induced homomorphisms of a group algebra , Annal of Math., t. 63, 1956 , p. 176-190. MR 18,197d | Zbl 0070.11601 · Zbl 0070.11601 · doi:10.2307/1969995
[25] JESSEN (B.) . - The theory of integration in a space of an intinite number of dimensions , Acta Math., t. 63, 1934 , p. 249-323. Zbl 0010.20004 | JFM 60.0328.01 · Zbl 0010.20004 · doi:10.1007/BF02547355
[26] JESSEN (B.) . - On strong differentiation in a space of infinitely many dimensions , Mat. Tidsskr., B, 1950 , p. 54-57. MR 12,324f | Zbl 0039.28701 · Zbl 0039.28701
[27] JESSEN (B.) . - On strong differentiation , Mat. Tidsskr., B. 1952 , p. 90-91. MR 14,855a | Zbl 0048.03903 · Zbl 0048.03903
[28] KAPPOS (Demetrios A.) . - Strukturtheorie der Wahrscheinlichkeitsfelder und -räume . - Berlin, Göttingen, Heidelberg, Springer Verlag, 1960 (Ergebnisse der Mathematik..., 24). Zbl 0092.33201 · Zbl 0092.33201
[29] KHINŇCIN (A. J.) . - Sur les théorèmes fondamentaux de la théorie de l’information [en russe] , Uspekhi mat. Nauk, t. 11, 1956 , p. 17-75. Traduction allemande dans Arbeiten zur Informationstheorie, I ; p. 26-85. - Berlin, V. E. B. Deutscher Verlag der Wissenschaften, 1957 .
[30] KOLMOGOROFF (A.) . - Untersuchungen über den Integralbegriff , Math. Annalen, t. 103, 1930 , p. 654-696. JFM 56.0923.01 · JFM 56.0923.01
[31] KRASNOSELSKIJ (A.) et RUTISKIJ (Ja. B.) . - Sur la théorie des espaces d’Orlicz [en russe] , Doklady Akad. Nauk S. S. S. R., N. S., t. 81, 1951 , p. 497-500. Zbl 0045.06101 · Zbl 0045.06101
[32] KRICKEBERG (K.) . - La nécessité de certaines hypothèses de Vitali fortes dans la théorie de la dérivation extrême de fonctions d’intervalles , C. R. Acad. Sc., t. 238, 1954 , p. 764-766. MR 15,610f | Zbl 0055.05104 · Zbl 0055.05104
[33] KRICKEBERG (K.) . - Extreme Derivierte von Zellenfunktionen in Booleschen \sigma -Algebren und ihre Integrtion , Sitzungb. math.-naturw. Kl. Bayer. Akad. Wiss. München, 1955 , p. 217-279. MR 18,118b | Zbl 0072.04501 · Zbl 0072.04501
[34] KRICKEBERG (K.) . - Convergence of martingales wih a directed index set , Trans. Amer. math. Soc., t. 83, 1956 , p. 313-337. MR 19,947e | Zbl 0083.27501 · Zbl 0083.27501 · doi:10.2307/1992878
[35] KRICKEBERG (K.) . - Stochastische Konvergenz von Semimartingalen , Math. Z., t. 66, 1957 , p. 470-486. MR 19,948a | Zbl 0083.27601 · Zbl 0083.27601 · doi:10.1007/BF01186623
[36] KRICKEBERG (K.) . - Stochastische Derivierte , Math. Nachr., t. 18, 1958 , p. 203-217. MR 21 #114 | Zbl 0083.27701 · Zbl 0083.27701 · doi:10.1002/mana.19580180123
[37] KRICKEBERG (K.) . - Seminar on martingales . - Aarhus, Matematisk Institut, Aarhus Universitet, 1959 , 58 p. · Zbl 0102.34704
[38] KRICKEBERG (K.) . - Notwendige Konvergenbedingungen bei Martingalen und verwandten Prozessen , Transactions of the Second Prague conference on information theory, statistical functions, random processes [ 1959 , Praguel]; p. 279-305. - Prague, Publishing House of the Czechoslovak Academy of Sciences, 1960 . Zbl 0100.13401 · Zbl 0100.13401
[39] KRICKEBERG (K.) . - Bemerkungen zur stochastischen Konvergenz , Bull. Soc. math. Grèce (à paraître). Zbl 0161.15202 · Zbl 0161.15202
[40] LA VALLÉE POUSSIN (C. de) . - Sur l’intégrale de Lebesgue , Trans. Amer. math. Soc., t. 16, 1915 , p. 435-501. JFM 45.0441.06 · JFM 45.0441.06
[41] LA VALLÉE POUSSIN (C. de) . - Intégrales de Lebesgue , fonctions d’ensemble, classes de Baire, 2e édition. - Paris, Gauthier-Villars, 1934 . Zbl 0009.20602 | JFM 60.0193.06 · Zbl 0009.20602
[42] LEADER (S.) . - The theory of Lp-space for finitely additive set functions , Annals of Math., t. 58, 1953 , p. 528-543. MR 15,326b | Zbl 0052.11401 · Zbl 0052.11401 · doi:10.2307/1969752
[43] LOÈVE (M.) . - Probability theory . Second edition. - Princeton, Toronto, New York, Van Nostrand Company, 1960 (The University Series in higher Mathematics). MR 23 #A670 | Zbl 0095.12201 · Zbl 0095.12201
[44] LOOMIS (L. H.) . - On the representation of \sigma -complete boolean algebras , Bull. Amer. math. Soc., t. 53, 1947 , p. 757-760. Article | MR 9,20b | Zbl 0033.01103 · Zbl 0033.01103 · doi:10.1090/S0002-9904-1947-08866-2
[45] MOY (Shu-Teh Chen) . - Measure extensions and the martingale convergence theorem , Proc. Amer. math. Soc., t. 4, 1953 , p. 902-907. MR 15,449a | Zbl 0052.36402 · Zbl 0052.36402 · doi:10.2307/2031827
[46] PAUC (C.) . - Ableitungsbasen , Prätopologie und starker Vitalischer Satz, J. für die reine und angew. Math., t. 191, 1953 , p. 69-91. MR 15,109d | Zbl 0050.27901 · Zbl 0050.27901 · doi:10.1515/crll.1953.191.69
[47] PAUC (C.) . - Contributions à une théorie de la différentiation de fonctions d’intervalle sans hypothèse de Vitali , C. R. Acad. Sc., t. 236, 1953 , p. 1937-1939. MR 15,205b | Zbl 0050.06004 · Zbl 0050.06004
[48] PAUC (C.) . - Dérivés et intégrants , Fonctions de cellule. Cours d’été de Varenne. - Varenna, 1954 (Publ. Mat. Ist. Roma, 76 p.). Zbl 0067.28302 · Zbl 0067.28302
[49] RUTOVITZ (D.) and PAUC (C.) . - Theory of Ward for cell functions , I and II, Annali di Mat., Série 4, t. 47, 1959 , p. 1-57. MR 22 #2675 | Zbl 0089.03501 · Zbl 0089.03501 · doi:10.1007/BF02410888
[50] SAKS (S.) . - Theory of the integral . Second edition. - Nex York, 1952 .
[51] SNELL (J. L.) . - Applications of martingale system theorems , Trans. Amer. math. Soc., t. 73, 1952 , p. 293-312. MR 14,295a | Zbl 0048.11402 · Zbl 0048.11402 · doi:10.2307/1990670
[52] SPARRE-ANDERSEN (E.) and JESSEN (B.) . - Some limit theorems on integrals in an abstract set , Danske Vid. Selsk. Math.-Fys. Medd., t. 22, 1946 , n^\circ 14, 29 p. MR 7,421d | Zbl 0063.07150 · Zbl 0063.07150
[53] WECKEN (Franz) . - Abstrakte Integrale und fastperiodische Funktionen , Math. Z., t. 45, 1939 , p. 377-404. MR 1,12b | Zbl 0021.22403 | JFM 65.0266.02 · Zbl 0021.22403 · doi:10.1007/BF01580291
[54] YOSIDA (K.) and HEWITT (E.) . - Finitely additive measures , Trans. Amer. math. Soc., t. 72, 1952 , p. 46-66. MR 13,543b | Zbl 0046.05401 · Zbl 0046.05401 · doi:10.2307/1990654
[55] ZAANEN (A. C.) . - Linear analysis ; measure and integral, Banach and Hilbert space, linear integral equations . - Amsterdam, North-Holland publishing Company ; Groningen, P. Noordhoff, 1953 (Biblioteca mathematica, 2). MR 15,878b | Zbl 0053.25601 · Zbl 0053.25601
[56] ZYGMUND (A.) . - On the differentiability of multiple integrals , Fund. Math., t. 23, 1934 , p. 143-149. Article | Zbl 0010.01404 | JFM 60.0219.02 · Zbl 0010.01404
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