×
Bru, B.; Heinich, H.

Sur l’esperance des variables aléatoires vectorielles. (French) Zbl 0472.60010

Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. B 16, 177-196 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0472.60010

Cited in 5 Documents

MSC:

60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60F15 Strong limit theorems
60G48 Generalizations of martingales

Keywords:

laws of large numbers; amarts
Cite Review PDF
Full Text: Numdam EuDML

References:

[1] K.A. Astbury , Amarts indexed by directed sets . Ann. Probability , t. 6 , n^\circ 2 , 1978 , p. 267 - 278 . Article | MR 464394 | Zbl 0378.60017 · Zbl 0378.60017 · doi:10.1214/aop/1176995572
[2] A. Bellow , On vector-valued asymptotic martingales . Proc. Nat. Acad. Sci. U. S. A. , t. 73 , 1976 , p. 1798 - 1799 . MR 407966 | Zbl 0366.60067 · Zbl 0366.60067 · doi:10.1073/pnas.73.6.1798
[3] A. Bellow , Les amarts uniformes . C. R. Acad. Sci. Paris , t. 284 , série A , 1977 , p. 1295 . MR 445602 | Zbl 0359.60047 · Zbl 0359.60047
[4] C. Bessaga , A. Pelczynski , On bases and unconditional convergence of series in Banach spaces . Studia Mathematica , t. 17 , 1958 , p. 151 - 164 . Article | MR 115069 | Zbl 0084.09805 · Zbl 0084.09805
[5] G. Birkhoff , Integration of functions with values in a Banach Space . Trans. Amer. Math. Soc. , t. 28 , 1935 , p. 357 - 378 . MR 1501815 | Zbl 0013.00803 | JFM 61.0234.01 · Zbl 0013.00803 · doi:10.2307/1989687
[6] N. Bourbaki , Éléments de Mathématiques , livre VI, Intégration, Chapitre 6, Hermann , Paris , 1959 . MR 124722 · Zbl 0102.25503
[7] B. Bru et H. Heinich , C. R. Acad. Sc. Paris , t. 288 , 1979 , p. 65 - 68 et p. 363 - 366 . Zbl 0397.60009 · Zbl 0397.60009
[8] R.V. Chacon et L. Sucheston , On convergence of vector-valued asymptotic martingales . Z. Wahrs. Verw. Gebiete , t. 33 , 1975 , p. 55 - 59 . MR 394859 | Zbl 0297.60005 · Zbl 0297.60005 · doi:10.1007/BF00539861
[9] S.D. Chatterji , Vector-valued martingales and their applications . Lectures notes , n^\circ 526 , Springer-Verlag , Berlin - Heidelberg - New York , 1976 , p. 33 - 51 . MR 517905 | Zbl 0336.60049 · Zbl 0336.60049
[10] A. Dvoretzky et C.A. Rogers , Absolute and unconditional convergence in normed linear spaces . Proc. Nat. Acad. Sci. U. S. A. , t. 36 , 1950 , p. 192 - 197 . MR 33975 | Zbl 0036.36303 · Zbl 0036.36303 · doi:10.1073/pnas.36.3.192
[11] G.A. Edgar et L. Sucheston , Amarts: a class of asymptotic martingales. A. Discrete parameter . J. Multiv. Anal. , t. 6 , 1976 , p. 193 - 221 . MR 413251 | Zbl 0336.60033 · Zbl 0336.60033 · doi:10.1016/0047-259X(76)90031-2
[12] G.A. Edgar et L. Sucheston , The Riesz decomposition for vector-valued amarts . Z. Wahrs. Verw. Gebiete , t. 36 , 1976 , p. 85 - 92 . MR 413252 | Zbl 0319.60025 · Zbl 0319.60025 · doi:10.1007/BF00533211
[13] N. Ghoussoub , Summability and vector-valued amarts , 1978 , - J. Multiv.An al . (à paraître). Zbl 0407.60043 · Zbl 0407.60043 · doi:10.1016/0047-259X(79)90076-9
[14] H. Heinich , Thèse , Université P.-et-M.-Curie , Paris VI, 1975 .
[15] M.E. Munroe , Absolute and unconditional convergence in Banach Space . Duke Math. J. , t. 13 , 1946 , p. 351 - 365 . Article | MR 19222 | Zbl 0063.04135 · Zbl 0063.04135 · doi:10.1215/S0012-7094-46-01330-0
[16] J. Neveu , Bases mathématiques du Calcul des Probabilités , Masson , Paris , 1964 . MR 198504 | Zbl 0137.11203 · Zbl 0137.11203
[17] J. Neveu , Martingales à temps discrets . Masson , Paris , 1974 .
[18] B.J. Pettis , On integration in vector space . Trans. Amer. Math. Soc. , t. 44 , 1938 , p. 277 - 304 . MR 1501970 | Zbl 0019.41603 | JFM 64.0371.02 · Zbl 0019.41603 · doi:10.2307/1989973
[19] H.H. Schaefer , Banach lattices and positive operators . Springer-Verlag , Berlin , Heidelberg , New York , 1974 . MR 423039 | Zbl 0296.47023 · Zbl 0296.47023
[20] E. Thomas , L’intégration par rapport à une mesure de Radon vectorielle . Ann. Inst. Fourier , t. 20 , 2 , 1970 , p. 55 - 191 . Numdam | MR 463396 | Zbl 0195.06101 · Zbl 0195.06101 · doi:10.5802/aif.352
[21] E. Thomas , The Lebesgue-Nikodym theorem for vector valued Radon measures . Amer. Math. Soc ., Memoir n^\circ 139, 1974 . Zbl 0282.28004 · Zbl 0282.28004
[22] E. Thomas , On some negative properties of the Pettis integral . Lecture Notes , n^\circ 541 . Springer-Verlag , Berlin , Heidelberg , New York , 1976 , p. 131 .
[23] J.J. Uhl , Pettis mean convergence of vector-valued asymptotic martingales . Z. Wahrs. Verw. Gebiete , t. 37 , 1977 , p. 291 - 295 . MR 571670 | Zbl 0325.60046 · Zbl 0325.60046 · doi:10.1007/BF00533421
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.