Martingales et dérivation

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1. [1] BOCHNER (S.). — Additive set functions on groups, Annals of Math., t. 40, 1939, p. 769-799. Zbl0024.04203MR1,110eJFM65.1317.01
2. [2] BOCHNER (S.) and PHILLIPS (R. S.). — Additive set functions and vector lattices, Annals of Math., t. 42, 1941, p. 316-324. Zbl0026.00104MR2,315dJFM67.0162.02
3. [3] BOCHNER (S.). — Partial ordering in the theory of martingales, Annals of Math., t. 62, 1955, p. 162-169. Zbl0068.11302MR17,167c
4. [4] CARATHÉODORY (C.). — Mass und Integral und ihre Algebraisierung. — Basel, Stuttgart, Birkhäuser Verlag, 1956 (Lehrbücher und Monographien..., Mathematische Reihe, 10). Zbl0074.04003MR18,117c
5. [5] CESARI (L.). — Surface area. — Princeton, Princeton University Press, 1956 (Annals of Mathematics Studies, 35). Zbl0073.04101MR17,596b
6. [6] CESARI (L.). — Area and measure. Brunswick, Summer Institute, 1958. 
7. [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. Zbl0080.12103
8. [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. Zbl0102.13402MR22 #12565
9. [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. Zbl0032.19602MR10,107a
10. [10] DIEUDONNÉ (J.). — Sur un théorème de Jessen, Fund. Math., t. 37, 1950, p. 242-248. Zbl0040.01902MR13,218d
11. [11] DOOB (J. L.). — Stochastic processes. — New York, J. Wiley ; London, Chapman and Hall, 1953 (Wiley Publications in Statistics). Zbl0053.26802MR15,445b
12. [12] DOOB (J. L.). — Semimartingales and subharmonic functions, Trans. Amer. math. Soc., t. 77, 1954, p. 86-121. Zbl0059.12205MR16,269a
13. [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. Zbl0126.14003
14. [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. Zbl0029.11503
15. [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. Zbl0061.25003MR3,207a
16. [16] FUGLEDE (B.). — On a theorem of F. Riesz, Math. Scand., t. 3, 1955, p. 283-302. Zbl0067.27901MR18,198b
17. [17]GOFFMAN (C.) and WATERMAN (D.). — On upper and lower limits in measure, Notices Amer, math. Soc., t. 5, 1958, p. 812. 
18. [18]HAHN (H.) and ROSENTHAL (A.). — Set functions. — Albuquerque, N. M., University of New Mexico Press, 1948. Zbl0033.05301MR9,504e
19. [19]HALMOS (P. R.). — Measure thoery. — Toronto, New York, London, Van Nostrand Company, 1950 (The University Series in higher Mathematics). 
20. [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). Zbl0064.04801
21. [21]HAUPT (O.) et PAUC (C.). — Propriétés de mesurabilité de bases de dérivation, PortugaliঠMath., t. 13, 1954, p. 37-54. Zbl0056.27601MR16,805a
22. [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. Zbl0068.04602MR17,719a
23. [23]HELMS (L. L.). — Mean convergence of martingales, Trans. Amer. math. Soc., t. 87, 1958, p. 439-446. Zbl0080.11904MR20 #1350
24. [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. Zbl0070.11601MR18,197d
25. [25]JESSEN (B.). — The theory of integration in a space of an intinite number of dimensions, Acta Math., t. 63, 1934, p. 249-323. Zbl0010.20004JFM60.0328.01
26. [26]JESSEN (B.). — On strong differentiation in a space of infinitely many dimensions, Mat. Tidsskr., B, 1950, p. 54-57. Zbl0039.28701MR12,324f
27. [27]JESSEN (B.). — On strong differentiation, Mat. Tidsskr., B. 1952, p. 90-91. Zbl0048.03903MR14,855a
28. [28]KAPPOS (Demetrios A.). — Strukturtheorie der Wahrscheinlichkeitsfelder und -räume. — Berlin, Göttingen, Heidelberg, Springer Verlag, 1960 (Ergebnisse der Mathematik..., 24). Zbl0092.33201
29. [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. [30]KOLMOGOROFF (A.). — Untersuchungen über den Integralbegriff, Math. Annalen, t. 103, 1930, p. 654-696. Zbl56.0923.01JFM56.0923.01
31. [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. Zbl0045.06101
32. [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. Zbl0055.05104MR15,610f
33. [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. Zbl0072.04501MR18,118b
34. [34]KRICKEBERG (K.). — Convergence of martingales wih a directed index set, Trans. Amer. math. Soc., t. 83, 1956, p. 313-337. Zbl0083.27501MR19,947e
35. [35]KRICKEBERG (K.). — Stochastische Konvergenz von Semimartingalen, Math. Z., t. 66, 1957, p. 470-486. Zbl0083.27601MR19,948a
36. [36]KRICKEBERG (K.). — Stochastische Derivierte, Math. Nachr., t. 18, 1958, p. 203-217. Zbl0083.27701MR21 #114
37. [37]KRICKEBERG (K.). — Seminar on martingales. — Aarhus, Matematisk Institut, Aarhus Universitet, 1959, 58 p. 
38. [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. Zbl0100.13401
39. [39]KRICKEBERG (K.). — Bemerkungen zur stochastischen Konvergenz, Bull. Soc. math. Grèce (à paraître). Zbl0161.15202
40. [40]LA VALLÉE POUSSIN (C. de). — Sur l'intégrale de Lebesgue, Trans. Amer. math. Soc., t. 16, 1915, p. 435-501. Zbl45.0441.06JFM45.0441.06
41. [41]LA VALLÉE POUSSIN (C. de). — Intégrales de Lebesgue, fonctions d'ensemble, classes de Baire, 2e édition. — Paris, Gauthier-Villars, 1934. Zbl0009.20602JFM60.0193.06
42. [42]LEADER (S.). — The theory of Lp-space for finitely additive set functions, Annals of Math., t. 58, 1953, p. 528-543. Zbl0052.11401MR15,326b
43. [43]LOÈVE (M.). — Probability theory. Second edition. — Princeton, Toronto, New York, Van Nostrand Company, 1960 (The University Series in higher Mathematics). Zbl0095.12201MR23 #A670
44. [44]LOOMIS (L. H.). — On the representation of σ-complete boolean algebras, Bull. Amer. math. Soc., t. 53, 1947, p. 757-760. Zbl0033.01103MR9,20b
45. [45]MOY (Shu-Teh Chen). — Measure extensions and the martingale convergence theorem, Proc. Amer. math. Soc., t. 4, 1953, p. 902-907. Zbl0052.36402MR15,449a
46. [46]PAUC (C.). — Ableitungsbasen, Prätopologie und starker Vitalischer Satz, J. für die reine und angew. Math., t. 191, 1953, p. 69-91. Zbl0050.27901MR15,109d
47. [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. Zbl0050.06004MR15,205b
48. [48]PAUC (C.). — Dérivés et intégrants, Fonctions de cellule. Cours d'été de Varenne. — Varenna, 1954 (Publ. Mat. Ist. Roma, 76 p.). Zbl0067.28302
49. [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. Zbl0089.03501MR22 #2675
50. [50]SAKS (S.). — Theory of the integral. Second edition. — Nex York, 1952. 
51. [51]SNELL (J. L.). — Applications of martingale system theorems, Trans. Amer. math. Soc., t. 73, 1952, p. 293-312. Zbl0048.11402MR14,295a
52. [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. Zbl0063.07150MR7,421d
53. [53]WECKEN (Franz). — Abstrakte Integrale und fastperiodische Funktionen, Math. Z., t. 45, 1939, p. 377-404. Zbl0021.22403MR1,12bJFM65.0266.02
54. [54]YOSIDA (K.) and HEWITT (E.). — Finitely additive measures, Trans. Amer. math. Soc., t. 72, 1952, p. 46-66. Zbl0046.05401MR13,543b
55. [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). Zbl0053.25601MR15,878b
56. [56]ZYGMUND (A.). — On the differentiability of multiple integrals, Fund. Math., t. 23, 1934, p. 143-149. Zbl0010.01404JFM60.0219.02

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