no. 1
Conical measures and vector measures
Annales de l'Institut Fourier, Tome 27 (1977) no. 1, pp. 83-105.

Toute mesure conique sur un espace faible complet E est représentée comme l’intégration par rapport à une mesure complètement additive sur la σ-algèbre cylindrique. Le lien entre les mesures coniques sur E et les mesures abstraites à valeurs dans E donne des conditions suffisantes pour que la mesure représentante soit finie.

Every conical measure on a weak complete space E is represented as integration with respect to a σ-additive measure on the cylindrical σ-algebra in E. The connection between conical measures on E and E-valued measures gives then some sufficient conditions for the representing measure to be finite.

@article{AIF_1977__27_1_83_0,
     author = {Kluv\'anek, Igor},
     title = {Conical measures and vector measures},
     journal = {Annales de l'Institut Fourier},
     pages = {83--105},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {27},
     number = {1},
     year = {1977},
     doi = {10.5802/aif.643},
     mrnumber = {57 #9936},
     zbl = {0311.28008},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.643/}
}
TY  - JOUR
AU  - Kluvánek, Igor
TI  - Conical measures and vector measures
JO  - Annales de l'Institut Fourier
PY  - 1977
SP  - 83
EP  - 105
VL  - 27
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.643/
DO  - 10.5802/aif.643
LA  - en
ID  - AIF_1977__27_1_83_0
ER  - 
%0 Journal Article
%A Kluvánek, Igor
%T Conical measures and vector measures
%J Annales de l'Institut Fourier
%D 1977
%P 83-105
%V 27
%N 1
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.643/
%R 10.5802/aif.643
%G en
%F AIF_1977__27_1_83_0
Kluvánek, Igor. Conical measures and vector measures. Annales de l'Institut Fourier, Tome 27 (1977) no. 1, pp. 83-105. doi : 10.5802/aif.643. http://www.numdam.org/articles/10.5802/aif.643/

[1] R. Anantharaman, On exposed points of the range of a vector measure, Vector and operator valued measures and applications (Proc. Sympos. Snowbird Resort, Alta, Utah ; 1972), p. 7-22. Academic Press, New York 1973. | Zbl

[2] R.G. Bartle, N. Dunford and J.T. Schwartz, Weak compactness and vector measures, Canad. J. Math., 7 (1955), 289-305. | MR | Zbl

[3] G. Choquet, Mesures coniques, affines et cylindriques, Symposia Mathematica, vol. II (INDAM, Roma, 1968) p. 145-182. Academic Press, London 1969. | Zbl

[4] G. Choquet, Lectures on Analysis, Edit. J. Marsden, T. Lance and S. Gelbart, W.A. Benjamin Inc. New York — Amsterdam 1969. | Zbl

[5] I. Kluvánek, The range of a vector-valued measure, Math. Systems Theory, 7 (1973), 44-54. | MR | Zbl

[6] I. Kluvánek, The extension and closure of vector measure, Vector and operator valued measures and applications (Proc. Sympos. Snowbird Resort, Alta, Utah ; 1972), p. 175-190. Academic Press, New York 1973. | Zbl

[7] I. Kluvánek, Characterization of the closed convex hull of the range of a vector-valued measure, J. Functional Analysis, 21 (1976), 316-329. | MR | Zbl

[8] I. Kluvánek, and G. Knowles, Vector measures and control systems, North Holland Publishing Co. Amsterdam 1975.

[9] V.I. Rybakov, Theorem of Bartle, Dunford and Schwartz concerning vector measures, Mat. Zametki, 7 (1970), 247-254 (English translation Math. Notes, 7 (1970), 147-151). | Zbl

[10] I.E. Segal, Equivalence of measure spaces, Amer. J. Math., 73 (1951), 275-313. | MR | Zbl

[11] J.J. Uhl, Extension and decomposition of vector measures, J. London Math., Soc., (2), 3 (1971), 672-676. | Zbl

Cité par Sources :