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Book Information

Author(s): Allen Gut and Klaus D. Schmidt
Title: Amarts and set function processes
Additional book information: Lecture Notes in Mathematics, vol. 1042, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983, 258 pp., $12.50. ISBN 3-540-12867-0

1.: E. S. Andersen and B. Jessen, Some limit theorems on set-functions, Danske Vid. Selsk. Math.-fys. Medd. 25, no. 5 (1948). MR 28376
2.: K. A. Astbury, Amarts indexed by directed sets, Ann. Probab. 6 (1978), 267-278. MR 464394
3.: D. G. Austin, G. A. Edgar and A. Ionescu Tulcea, Pointwise convergence in terms of expectations, Z. Wahrsch. verw. Gebiete 30 (1974), 17-26. MR 358945
4.: S. D. Bagchi, Almost sure convergence of classes of multivalued asymptotic martingales, Ann. Inst. H. Poincaré Sect. B (to appear).
5.: J. R. Baxter, Pointwise in terms of weak convergence, Proc. Amer. Math. Soc. 46 (1974), 395-398. MR 380968
6.: A. Bellow, On vector-valued asymptotic martingales, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 1798-1799. MR 407966
7.: A. Bellow, Uniform amarts: A class of asymptotic martingales for which strong almost sure convergence obtains, Z. Wahrsch. verw. Gebiete 41 (1978), 177-191. MR 471065
8.: A. Bellow, For historical record, Proc. 1983 Oberwolfach Conf. on Measure Theory, Lecture Notes in Math., vol. 1089, Springer-Verlag (to appear).
9.: A. Brunel and U. Krengel, Parier avec un prophète dans le cas d'un processus sous-additif, C. R. Acad. Sci. Paris Sér. A 288 (1979), 57-60. MR 522020
10.: A. Brunel and L. Sucheston, Sur les amarts faibles à valeurs vectorielles, C. R. Acad. Sci. Paris Sér. A 282 (1976), 1011-1014. MR 415761
11.: A. Brunel and L. Sucheston, Une caractérisation probabiliste de la séparabilité du dual d 'un espace de Banach, C. R. Acad. Sci. Paris Sér. A 282 (1977), 1469-1472. MR 440694
12.: R. V. Chacon, A "stopped" proof of convergence, Adv. in Math. 14 (1974), 365-368. MR 365688
13.: R. V. Chacon and L. Sucheston, On convergence of vector-valued asymptotic martingales, Z. Wahrsch. verw Gebiete 33 (1975), 55-59. MR 394859
14.: S. D. Chatterji, Martingale convergence and Radon-Nikodym theorem in Banach spaces, Math. Scand. 22 (1968), 21-41. MR 246341
15.: B. D. Choi and L. Sucheston, Continuous parameter uniform amarts, Probability in Banach Spaces. III, Lecture Notes in Math., vol. 860, Springer-Verlag, 1981, pp. 85-98. MR 647956
16.: W. J. Davis and W. B. Johnson, Weakly convergent sequences of Banach space valued random variables, Banach Spaces of Analytic Functions, Lecture Notes in Math., vol. 604, Springer-Verlag, 1977, pp. 29-31. MR 458167
17.: J. L. Doob, Stochastic processes, Wiley, New York, 1953. MR 58896
18.: A. Dvoretzky, On stopping time directed convergence, Bull. Amer. Math. Soc. 82 (1976), 347-349. MR 415760
19.: G. A. Edgar, Asplund operators and a. e. convergence, J. Multivariate Anal. 10 (1980), 460-466. MR 588087
20.: G. A. Edgar, Additive amarts, Ann. Probab. 10 (1982), 199-206. MR 637386
21.: G. A. Edgar and L. Sucheston, Amarts: A class of asymptotic martingales. I, II, J. Multivariate Anal. 6 (1976), 196-221, 572-591. MR 431370
22.: G. A. Edgar, The Riesz decomposition for vector-valued amarts, Z. Wahrsch. verw. Gebiete 36 (1976), 85-92. MR 413252
23.: G. A. Edgar, Démonstrations de lois des grands nombres par les sous-martingales descendantes, C. R. Acad. Sci. Paris Sér. I 292 (1981), 967-969. MR 631108
24.: N. Frangos, On regularity of Banach valued processes, Ann. Probab. (to appear). MR 799433
25.: N. Ghoussoub and L. Sucheston, A refinement of the Riesz decomposition for amarts and semiamarts, J. Multivariate Anal. 8 (1978), 146-150. MR 494474
26.: A. and C. Ionescu Tulcea, Abstract ergodic theorems, Trans. Amer. Math. Soc. 107 (1963), 313-337. MR 150611
27.: K. Krickeberg, Convergence of martingales with a directed index set, Trans. Amer. Math. Soc. 83 (1956), 313-337. MR 91328
28.: K. Krickeberg, Notwendige Konvergenzbedingungen bei Martingalen und verwandten processen, Trans. 2nd Prague Conf. on Information theory (Czech. Acad. Sci., Prague, 1959), pp. 279-305. MR 126294
29.: C. W. Lamb, A ratio limit theorem for approximate martingales, Canad. J. Math. 25 (1973), 772-779. MR 331503
30.: P. A. Meyer, Probabilities and potential, Blaisdell, Waltham, Mass., 1966.
31.: A. Millet, Sur la caractérisation des conditions de Vitali par la convergence essentielle des martingales, C. R. Acad. Sci. Paris Sér. A 287 (1978), 887-890. MR 551772
32.: A. Millet, Convergence and regularity of strong submartingales, Processus Aleatoires à Deux Indices, Lecture Notes in Math., vol. 863, Springer-Verlag, 1981, pp. 50-58. MR 630305
33.: A. Millet and L. Sucheston, La convergence essentielle des martingales bornées dans L, C. R. Acad. Sci. Paris Sér. A 288 (1979), 595-598. MR 531590
34.: A. Millet and L. Sucheston, Characterizations of Vitali conditions with overlap in terms of convergence of classes at amarts, Canad. J. Math 31 (1979), 1033-1046. MR 546956
35.: A. Millet and L. Sucheston, Convergence of classes of amarts indexed by directed sets, Canad. J. Math. 32 (1980), 86-125. MR 559789
36.: A. Millet and L. Sucheston, On convergence of L, Probab. Math. Statist. 1 (1980), 151-169. MR 626308
37.: A. Millet and L. Sucheston, On regularity of multiparameter amarts and martingales, Z. Wahrsch. verw. Gebiete 56 (1981), 21-45. MR 612158
38.: J. Neveu, Convergence presque sur des martingales multivoques, Ann. Inst. Poncaré Sect. B. 8 (1972), 1-7. MR 331504
39.: J. Neveu, Discrete-parameter martingales, North-Holland, Amsterdam, 1975. MR 402915
40.: W. D. Sudderth, A "Fatou 's equation" for randomly stopped variables, Ann. Math. Statist. 42 (1971), 2143-2146. MR 300370
41.: M. Talagrand, Some structure results for martingales in the limit and pramarts, Ann. Probab. (to appear). MR 806217
42.: M. Talagrand, Derivation, L, Trans. Amer. Math. Soc. (to appear). MR 596876

Review Information:
Journal: Bull. Amer. Math. Soc. 12 (1985), 306-312.
DOI: 10.1090/S0273-0979-1985-15387-X
PII: S 0273-0979(1985)15387-X

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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