Conical measures and vector measures

Igor Kluvánek

Annales de l'institut Fourier (1977)

  • Volume: 27, Issue: 1, page 83-105
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Kluvánek, Igor. "Conical measures and vector measures." Annales de l'institut Fourier 27.1 (1977): 83-105. <http://eudml.org/doc/74312>.

@article{Kluvánek1977,
abstract = {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.},
author = {Kluvánek, Igor},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {83-105},
publisher = {Association des Annales de l'Institut Fourier},
title = {Conical measures and vector measures},
url = {http://eudml.org/doc/74312},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Kluvánek, Igor
TI - Conical measures and vector measures
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 1
SP - 83
EP - 105
AB - 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.
LA - eng
UR - http://eudml.org/doc/74312
ER -

References

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  1. [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. Zbl0288.28015
  2. [2] R.G. BARTLE, N. DUNFORD and J.T. SCHWARTZ, Weak compactness and vector measures, Canad. J. Math., 7 (1955), 289-305. Zbl0068.09301MR16,1123c
  3. [3] G. CHOQUET, Mesures coniques, affines et cylindriques, Symposia Mathematica, vol. II (INDAM, Roma, 1968) p. 145-182. Academic Press, London 1969. Zbl0187.06901
  4. [4] G. CHOQUET, Lectures on Analysis, Edit. J. Marsden, T. Lance and S. Gelbart, W.A. Benjamin Inc. New York — Amsterdam 1969. Zbl0181.39602
  5. [5] I. KLUVÁNEK, The range of a vector-valued measure, Math. Systems Theory, 7 (1973), 44-54. Zbl0256.28008MR48 #495
  6. [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. Zbl0302.28009
  7. [7] I. KLUVÁNEK, Characterization of the closed convex hull of the range of a vector-valued measure, J. Functional Analysis, 21 (1976), 316-329. Zbl0317.46035MR53 #14123
  8. [8] I. KLUVÁNEK, and G. KNOWLES, Vector measures and control systems, North Holland Publishing Co. Amsterdam 1975. Zbl0316.46043
  9. [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). Zbl0198.47801
  10. [10] I.E. SEGAL, Equivalence of measure spaces, Amer. J. Math., 73 (1951), 275-313. Zbl0042.35502MR12,809f
  11. [11] J.J. UHL, Extension and decomposition of vector measures, J. London Math., Soc., (2), 3 (1971), 672-676. Zbl0213.33901

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