Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$ L\sb{0}$-valued vector measures are bounded


Authors: N. J. Kalton, N. T. Peck and James W. Roberts
Journal: Proc. Amer. Math. Soc. 85 (1982), 575-582
MSC: Primary 46G10; Secondary 28B05
DOI: https://doi.org/10.1090/S0002-9939-1982-0660628-X
MathSciNet review: 660628
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Every vector measure taking values in $ {L_0}(0,1)$ has bounded range.


References [Enhancements On Off] (What's this?)

  • [1] K. Bichteler, Stochastic integrators, Bull. Amer. Math. Soc. 1 (1979), 761-765. MR 537627 (82k:60122)
  • [2] J. Diestel and J. J. Uhl, Vector measures, Math. Surveys, no. 15, Amer. Math. Soc., Providence, R. I., 1977. MR 0453964 (56:12216)
  • [3] W. Fisher and U. Scholer, The range of vector measures into Orlicz spaces, Studia Math. 59 (1976), 53-61. MR 0427580 (55:611)
  • [4] -, Sur la bornitude d'une mesure vectorielle, C. R. Acad. Sci. Paris Sér. A 282 (1976), 519-522.
  • [5] N. J. Kalton, Linear operators on $ {L_p}$ for $ 0 < p < 1$, Trans. Amer. Math. Soc. 259 (1980), 319-355. MR 567084 (81d:47022)
  • [6] N. J. Kalton and J. W. Roberts, The Maharam problem and connections with the theory of $ F$-spaces (in preparation).
  • [7] B. S. Kašhin, The stability of unconditional almost everywhere convergence, Mat. Zametki 14 (1973), 645-654. (Russian) MR 0330400 (48:8737)
  • [8] S. Kwapien, On the form of alinear operator in the space of all measurable functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 951-954. MR 0336313 (49:1088)
  • [9] I. Labuda, Ensembles convexes dans les espaces d'Orlicz, C. R. Acad. Sci. Paris Sér. A 281 (1975), 443-445. MR 0417771 (54:5819)
  • [10] D. Maharam, An algebraic characterization of measure algebras, Ann of Math. (2) 48 (1947), 154-157. MR 0018718 (8:321b)
  • [11] B. Maurey, Theórèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces de $ {L_p}$, Asterisque Sér. A 11 (1974), 39-42.
  • [12] B. Maurey and G. Pisier, Un théorème d'extrapolation et ses conséquences, C. R. Acad. Sci. Paris Sér. A 277 (1973), 39-42.
  • [13] M. Metivier and J. Pellaumail, Measures stochastiques à valeurs dans les espaces $ {L_0}$, Z. Wahrsch. Verw. Gebiete 40 (1977), 101-114. MR 0471080 (57:10820)
  • [14] P. A. Meyer, Characterisation des semimartingales, d'apres Dellacherie, Lecture Notes in Math., vol. 721, Springer-Verlag, New York, 1979, pp. 620-623. MR 544830 (81c:60064)
  • [15] K. Musial, C. Ryll-Nardzewski and W. A. Woyczyński, Convergence presque sûre des séries aléatoires vectorielles à multiplicateurs bornés, C. R. Acad. Sci. Paris Sér. A 279 (1974), 225-- 228. MR 0378019 (51:14188)
  • [16] E. M. Nikišin, Resonance theorems and superlinear opeators, Uspehi Mat. Nauk 25 (1970), 129-191; English transl., Russian Math. Surveys 25 (1970), 124-187. MR 0296584 (45:5643)
  • [17] P. Turpin, Une mesure vectorielle non bornée, C. R. Acad. Sci. Paris Sér. A 280 (1975), 509-511. MR 0385556 (52:6417)
  • [18] -, Convexités dans les espaces vectoriels topologiques généraux, Dissertationes Math. 136 (1976).
  • [19] M. Talagrand, Les mesures vectorielles à valeurs dans $ {L_0}$ sont bornées (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G10, 28B05

Retrieve articles in all journals with MSC: 46G10, 28B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0660628-X
Keywords: $ {L_0}$-valued vector measure, bounded vector measure, control submeasure, unbounded support of a vector measure, finite algebra of measurable sets
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society