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 $\sigma$-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 $\sigma$-additive measure on the cylindrical $\sigma$-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},
volume = {27},
number = {1},
year = {1977},
doi = {10.5802/aif.643},
zbl = {0311.28008},
mrnumber = {57 #9936},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.643/}
}
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 0288.28015

[2] R.G. Bartle, N. Dunford and J.T. Schwartz, Weak compactness and vector measures, Canad. J. Math., 7 (1955), 289-305. | MR 16,1123c | Zbl 0068.09301

[3] G. Choquet, Mesures coniques, affines et cylindriques, Symposia Mathematica, vol. II (INDAM, Roma, 1968) p. 145-182. Academic Press, London 1969. | Zbl 0187.06901

[4] G. Choquet, Lectures on Analysis, Edit. J. Marsden, T. Lance and S. Gelbart, W.A. Benjamin Inc. New York — Amsterdam 1969. | Zbl 0181.39602

[5] I. Kluvánek, The range of a vector-valued measure, Math. Systems Theory, 7 (1973), 44-54. | MR 48 #495 | Zbl 0256.28008

[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 0302.28009

[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 53 #14123 | Zbl 0317.46035

[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 0198.47801

[10] I.E. Segal, Equivalence of measure spaces, Amer. J. Math., 73 (1951), 275-313. | MR 12,809f | Zbl 0042.35502

[11] J.J. Uhl, Extension and decomposition of vector measures, J. London Math., Soc., (2), 3 (1971), 672-676. | Zbl 0213.33901