$L_{0}$-valued vector measures are bounded
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- by N. J. Kalton, N. T. Peck and James W. Roberts
- Proc. Amer. Math. Soc. 85 (1982), 575-582
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660628-X
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Abstract:
Every vector measure taking values in ${L_0}(0,1)$ has bounded range.References
- Klaus Bichteler, Stochastic integrators, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 5, 761–765. MR 537627, DOI 10.1090/S0273-0979-1979-14655-X
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
- Werner Fischer and Ulrich Schöler, The range of vector measures into Orlicz spaces, Studia Math. 59 (1976), no. 1, 53–61. MR 427580, DOI 10.4064/sm-59-1-53-61 —, Sur la bornitude d’une mesure vectorielle, C. R. Acad. Sci. Paris Sér. A 282 (1976), 519-522.
- N. J. Kalton, Linear operators on $L_{p}$ for $0<p<1$, Trans. Amer. Math. Soc. 259 (1980), no. 2, 319–355. MR 567084, DOI 10.1090/S0002-9947-1980-0567084-3 N. J. Kalton and J. W. Roberts, The Maharam problem and connections with the theory of $F$-spaces (in preparation).
- B. S. Kašin, The stability of unconditional almost everywhere convergence, Mat. Zametki 14 (1973), 645–654 (Russian). MR 330400
- S. Kwapień, On the form of a linear operator in the space of all measurable functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 951–954 (English, with Russian summary). MR 336313
- Iwo Labuda, Ensembles convexes dans les espaces d’Orlicz, C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 12, Aii, A443–A445 (French, with English summary). MR 417771
- Dorothy Maharam, An algebraic characterization of measure algebras, Ann. of Math. (2) 48 (1947), 154–167. MR 18718, DOI 10.2307/1969222 B. Maurey, Theórèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces de ${L_p}$, Asterisque Sér. A 11 (1974), 39-42. B. Maurey and G. Pisier, Un théorème d’extrapolation et ses conséquences, C. R. Acad. Sci. Paris Sér. A 277 (1973), 39-42.
- M. Métivier and J. Pellaumail, Mesures stochastiques à valeurs dans des espaces $L_{0}$, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40 (1977), no. 2, 101–114 (French, with English summary). MR 471080, DOI 10.1007/BF00532875
- P.-A. Meyer, Caractérisation des semimartingales, d’après Dellacherie, Séminaire de Probabilités, XIII (Univ. Strasbourg, Strasbourg, 1977/78) Lecture Notes in Math., vol. 721, Springer, Berlin, 1979, pp. 620–623 (French). MR 544830
- Kazimierz Musiał, Czeslaw Ryll-Nardzewski, and Wojbor A. Woyczyński, Convergence presque sûre des séries aléatoires vectorielles à multiplicateurs bornés, C. R. Acad. Sci. Paris Sér. A 279 (1974), 225–228 (French). MR 378019
- E. M. Nikišin, Resonance theorems and superlinear operators, Uspehi Mat. Nauk 25 (1970), no. 6(156), 129–191 (Russian). MR 0296584
- Philippe Turpin, Une mesure vectorielle non bornée, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), A509–A511 (French). MR 385556 —, Convexités dans les espaces vectoriels topologiques généraux, Dissertationes Math. 136 (1976). M. Talagrand, Les mesures vectorielles à valeurs dans ${L_0}$ sont bornées (to appear).
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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