Martingales et dérivation

Krickeberg, K.; Pauc, C.

Bulletin de la Société Mathématique de France, Tome 91 (1963), pp. 455-543.

[1] Bochner (S.). - Additive set functions on groups, Annals of Math., t. 40, 1939, p. 769-799. | JFM | MR | Zbl

[2] Bochner (S.) and Phillips (R. S.). - Additive set functions and vector lattices, Annals of Math., t. 42, 1941, p. 316-324. | JFM | MR | Zbl

[3] Bochner (S.). - Partial ordering in the theory of martingales, Annals of Math., t. 62, 1955, p. 162-169. | MR | Zbl

[4] Carathéodory (C.). - Mass und Integral und ihre Algebraisierung. - Basel, Stuttgart, Birkhäuser Verlag, 1956 (Lehrbücher und Monographien..., Mathematische Reihe, 10). | MR | Zbl

[5] Cesari (L.). - Surface area. - Princeton, Princeton University Press, 1956 (Annals of Mathematics Studies, 35). | MR | Zbl

[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

[8] Chow (Y. S.). - Martingales in a σ-finite measure space indexed by directed sets, Trans. Amer. math. Soc., t. 97, 1960, p. 254-285. | MR | Zbl

[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 | Zbl

[10] Dieudonné (J.). - Sur un théorème de Jessen, Fund. Math., t. 37, 1950, p. 242-248. | MR | Zbl

[11] Doob (J. L.). - Stochastic processes. - New York, J. Wiley ; London, Chapman and Hall, 1953 (Wiley Publications in Statistics). | MR | Zbl

[12] Doob (J. L.). - Semimartingales and subharmonic functions, Trans. Amer. math. Soc., t. 77, 1954, p. 86-121. | MR | Zbl

[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

[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

[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. | MR | Zbl

[16] Fuglede (B.). - On a theorem of F. Riesz, Math. Scand., t. 3, 1955, p. 283-302. | MR | Zbl

[17]Goffman (C.) and Waterman (D.). - On upper and lower limits in measure, Notices Amer, math. Soc., t. 5, 1958, p. 812.

[18]Hahn (H.) and Rosenthal (A.). - Set functions. - Albuquerque, N. M., University of New Mexico Press, 1948. | MR | Zbl

[19]Halmos (P. R.). - Measure thoery. - Toronto, New York, London, Van Nostrand Company, 1950 (The University Series in higher Mathematics).

[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

[21]Haupt (O.) et Pauc (C.). - Propriétés de mesurabilité de bases de dérivation, PortugaliঠMath., t. 13, 1954, p. 37-54. | MR | Zbl

[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 | Zbl

[23]Helms (L. L.). - Mean convergence of martingales, Trans. Amer. math. Soc., t. 87, 1958, p. 439-446. | MR | Zbl

[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 | Zbl

[25]Jessen (B.). - The theory of integration in a space of an intinite number of dimensions, Acta Math., t. 63, 1934, p. 249-323. | JFM | Zbl

[26]Jessen (B.). - On strong differentiation in a space of infinitely many dimensions, Mat. Tidsskr., B, 1950, p. 54-57. | MR | Zbl

[27]Jessen (B.). - On strong differentiation, Mat. Tidsskr., B. 1952, p. 90-91. | MR | Zbl

[28]Kappos (Demetrios A.). - Strukturtheorie der Wahrscheinlichkeitsfelder und -räume. - Berlin, Göttingen, Heidelberg, Springer Verlag, 1960 (Ergebnisse der Mathematik..., 24). | MR | Zbl

[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

[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

[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 | Zbl

[33]Krickeberg (K.). - Extreme Derivierte von Zellenfunktionen in Booleschen σ-Algebren und ihre Integrtion, Sitzungb. math.-naturw. Kl. Bayer. Akad. Wiss. München, 1955, p. 217-279. | MR | Zbl

[34]Krickeberg (K.). - Convergence of martingales wih a directed index set, Trans. Amer. math. Soc., t. 83, 1956, p. 313-337. | MR | Zbl

[35]Krickeberg (K.). - Stochastische Konvergenz von Semimartingalen, Math. Z., t. 66, 1957, p. 470-486. | MR | Zbl

[36]Krickeberg (K.). - Stochastische Derivierte, Math. Nachr., t. 18, 1958, p. 203-217. | MR | Zbl

[37]Krickeberg (K.). - Seminar on martingales. - Aarhus, Matematisk Institut, Aarhus Universitet, 1959, 58 p.

[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

[39]Krickeberg (K.). - Bemerkungen zur stochastischen Konvergenz, Bull. Soc. math. Grèce (à paraître). | Zbl

[40]La Vallée Poussin (C. De). - Sur l'intégrale de Lebesgue, Trans. Amer. math. Soc., t. 16, 1915, p. 435-501. | JFM

[41]La Vallée Poussin (C. De). - Intégrales de Lebesgue, fonctions d'ensemble, classes de Baire, 2e édition. - Paris, Gauthier-Villars, 1934. | JFM | Zbl

[42]Leader (S.). - The theory of Lp-space for finitely additive set functions, Annals of Math., t. 58, 1953, p. 528-543. | MR | Zbl

[43]Loève (M.). - Probability theory. Second edition. - Princeton, Toronto, New York, Van Nostrand Company, 1960 (The University Series in higher Mathematics). | MR | Zbl

[44]Loomis (L. H.). - On the representation of σ-complete boolean algebras, Bull. Amer. math. Soc., t. 53, 1947, p. 757-760. | MR | Zbl

[45]Moy (Shu-Teh Chen). - Measure extensions and the martingale convergence theorem, Proc. Amer. math. Soc., t. 4, 1953, p. 902-907. | MR | Zbl

[46]Pauc (C.). - Ableitungsbasen, Prätopologie und starker Vitalischer Satz, J. für die reine und angew. Math., t. 191, 1953, p. 69-91. | MR | Zbl

[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 | Zbl

[48]Pauc (C.). - Dérivés et intégrants, Fonctions de cellule. Cours d'été de Varenne. - Varenna, 1954 (Publ. Mat. Ist. Roma, 76 p.). | Zbl

[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 | Zbl

[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 | Zbl

[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° 14, 29 p. | MR | Zbl

[53]Wecken (Franz). - Abstrakte Integrale und fastperiodische Funktionen, Math. Z., t. 45, 1939, p. 377-404. | JFM | MR | Zbl

[54]Yosida (K.) and Hewitt (E.). - Finitely additive measures, Trans. Amer. math. Soc., t. 72, 1952, p. 46-66. | MR | Zbl

[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 | Zbl

[56]Zygmund (A.). - On the differentiability of multiple integrals, Fund. Math., t. 23, 1934, p. 143-149. | JFM | Zbl