Amarts of finite order and Pettis Cauchy sequences of Bochner integrable functions in locally convex spaces

Dinh Quang Luu

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications (1985)

  • Volume: 85, Issue: 3, page 91-106
  • ISSN: 0246-1501

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Dinh Quang Luu. "Amarts of finite order and Pettis Cauchy sequences of Bochner integrable functions in locally convex spaces." Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications 85.3 (1985): 91-106. <http://eudml.org/doc/80621>.

@article{DinhQuangLuu1985,
author = {Dinh Quang Luu},
journal = {Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications},
keywords = {Hausdorff locally convex quasi-complete space; amart of finite order; Pettis mean convergence theorems},
language = {eng},
number = {3},
pages = {91-106},
publisher = {UER de Sciences exactes et naturelles de l'Université de Clermont},
title = {Amarts of finite order and Pettis Cauchy sequences of Bochner integrable functions in locally convex spaces},
url = {http://eudml.org/doc/80621},
volume = {85},
year = {1985},
}

TY - JOUR
AU - Dinh Quang Luu
TI - Amarts of finite order and Pettis Cauchy sequences of Bochner integrable functions in locally convex spaces
JO - Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
PY - 1985
PB - UER de Sciences exactes et naturelles de l'Université de Clermont
VL - 85
IS - 3
SP - 91
EP - 106
LA - eng
KW - Hausdorff locally convex quasi-complete space; amart of finite order; Pettis mean convergence theorems
UR - http://eudml.org/doc/80621
ER -

References

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  1. [1] C. Blondia, Locally convex spaces with the Radon-Nikodym property, Math. Nachr, 114(1983) 335-341. Zbl0557.46015MR745066
  2. [2] B. Bru, H. Heinich, Sur l'espérance des variables aléatoires vectorielles. Ann. Inst. Henri Poincaré, Vol. XVI, n° 3 (1980) 177-196. Zbl0472.60010MR595198
  3. [3] C. Castaing, M. Valadier, Convex analysis and measurable multifunctions. Lecture Notes in Math. N° 580, Springer-Verlag1977. Zbl0346.46038MR467310
  4. [4] R.V. Chacon, L. Sucheston, On convergence of vector-valued asymptotic martingales, Z. Wahrsch. Verw. Gebiete33 (1975) 55-59. Zbl0297.60005MR394859
  5. [5] G.Y.H. Chi, On the Radon-Nikodym theorem and locally convex spaces with the Radon-Nikodym property. Proc. Amer. Math. Soc. Vol. 62, n° 2 (1977) 245-253. Zbl0348.46033MR435338
  6. [6] G.A. Edgar, L. Sucheston, Amarts: A class of asymptotic martingales (Discrete parameter). J. Multiv. Anal.6 (1976) 193-221. Zbl0336.60033MR413251
  7. [7] L. Egghe, The Radon-Nikodym property, σ-dentability and martingales in locally convex spaces. Pac. Jour. Math. Vol. 87, N° 2 (1980) 335-341. Zbl0393.60005
  8. [8] J. Hoffmann-Jørgensen, Vector measures. Math. Scand.28 (1971)5-32. Zbl0217.38001MR306438
  9. [9] Dinh Quang Luu, Applications of set-valued Radon-Nikodym theorems to convergence of multivalued L1-amarts. Math. Scand.54(1984) 101-113. Zbl0562.60057MR753067
  10. [10] Dinh Quang Luu, The Radon-Nikodym property and convergence of amarts in Fréchet spaces. Ann. Inst. Clermont, Sér. Prob. Statist. N° 3, to appear. Zbl0568.60045
  11. [11] J. Neveu, Martingales à temps discrets. Masson Cie, Paris1972. MR402914
  12. [12] A. Pietsch, Nuclear locally convex spaces. Springer-Verlag, Berlin66, 1972. Zbl0236.46001MR350360
  13. [13] Jr. Uhl J.J., Pettis mean convergence of vector-valued asymptotic martingales. Z. Wahrsch. Verw. Gebiete37(1977) 291-295. Zbl0325.60046MR571670

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