Publication: The Radon-Nikodým theorem in bornological spaces. (Spanish: El teorema de Radon-Nikodym en espacios bornológicos).
Loading...
Full text at PDC
Publication Date
1981
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Real Academia de Ciencias Exactas, Físicas y Naturales
Citations
Exportar
Abstract
The author presents some Radon-Nikodým theorems—i.e., if (Ω,Σ,μ) is a finite measurable space and m is a μ -continuous vector measure then {m(A)/μ(A):A∈Σ} being compact in some sense implies that m is an integral. Theorem 6: One has a Radon-Nikodým theorem for Fréchet spaces. Theorem 8: One has a Radon-Nikodým theorem for vector measures of finite variation and for a quasicomplete space E with the metrizable Pietsch property. (E is said to have the metrizable Pietsch property if X⊂E N with ∑p(x n )<∞ for each (x n )∈X and each continuous seminorm p implies the existence of a B , B⊂E , absolutely convex, bounded and metrizable, with gauge P B , and such that ∑P B (y n )≤1 for each (y n )∈X .) G. Y. H. Chi proved this result [Measure theory (Oberwolfach, 1975), pp. 199–210, Lecture Notes in Math., 541, Springer, Berlin, 1976; with a compactness hypothesis for m(A)/μ(A) , instead of weak compactness. Unfortunately the proofs are not quite clear or even quite exact. In the reference to the Grothendieck book there is a B instead of an 8.
Description
UCM subjects
Unesco subjects
Keywords
Citation
BOMBAL GORDON, F. (1981). Medida e integración en espacios bornológicos. Rev. R. Acad. Ci. Madrid, 75, 115-138.
CHI, G. Y. H. (1975). A geometrie characterization of Fréchet spaces with the Radon-Nikodym property. Proc. Of the Amer. Math. Soc., 48, 371-380.
CHI, G. Y. H. (1976). On the Radon-Nikodym theorem in locally convex spaces. En “Measure theory”, Lect. Notes in Math., n.° 541. Springer, Berlin.
DIESTEL, J. and UHL, J. Jr. (1977). Vector Measures. Math. Surveys, 15. Amer. Math. Soc., Providence, R. I.
GILLIAM, D. (1976). Geometry and the Radon-Nikodym theorem in strict Mackey convergence spaces. Pacific Journal of Math., 65, 353-364.
GROTHENDIECK, A. (1973). Topological vector spaces. Gordon and Breach, New York.
HOGBE-NLEND, H. (1971). Théorie des bornologies et applications. Lect. Notes in Math., n.° 213. Springer, Berlin.
LARMAN, D. G. and ROGERS, C. A. (1973). The normability of metrizable sets. Bull. London Math. Soc., 5, 39-48.
METIVIER, M. (1967). Martingales á valeurs vectorielles. Applications á la dérivation des mesures vectorielles. Ann. Inst. Fourier, 2, 175-208.
MOEDANO,S.and UHL,J.Jr.(1971). Radon-Nikodym theorems for thé Bochner and Pettis integrals.Pac.J.of Math., 38, 531-536.
PIETSCH, A. (1972). Nuclear locally convex spaces. Springer, Berlin.
RIEFFEL, M. A. (1968). The Radon-Nikodym theorem for the Bochner integral. Trans. Amer. Math. Soc., J31, 466-487.
SAAB, E. (1976). Sur la propriété de Radon-Nikodym dans les spaces localement convexes de type (BM). C. R. Acad. Paris, t. 283, Ser. A, 899-902.
SCHAEFER, H. H. (1971). Topological vector spaces. Springer, Berlin.