A continuous version of Liapunov's convexity theorem

Arrigo Cellina; Giovanni Colombo; Alessandro Fonda

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 1, page 23-36
  • ISSN: 0294-1449

How to cite


Cellina, Arrigo, Colombo, Giovanni, and Fonda, Alessandro. "A continuous version of Liapunov's convexity theorem." Annales de l'I.H.P. Analyse non linéaire 5.1 (1988): 23-36. <http://eudml.org/doc/78145>.

author = {Cellina, Arrigo, Colombo, Giovanni, Fonda, Alessandro},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Liapunov's convexity theorem; constant selection},
language = {eng},
number = {1},
pages = {23-36},
publisher = {Gauthier-Villars},
title = {A continuous version of Liapunov's convexity theorem},
url = {http://eudml.org/doc/78145},
volume = {5},
year = {1988},

AU - Cellina, Arrigo
AU - Colombo, Giovanni
AU - Fonda, Alessandro
TI - A continuous version of Liapunov's convexity theorem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 1
SP - 23
EP - 36
LA - eng
KW - Liapunov's convexity theorem; constant selection
UR - http://eudml.org/doc/78145
ER -


  1. [1] A. Fryszkowski, Continuous Selections for a Class of Non-Convex Multivalued Maps, Studia Mathematica, T. LXXVI, 1983, pp. 163-174. Zbl0534.28003MR730018
  2. [2] P. Halmos, The Range of a Vector Measure, Bull. Am. Math. Soc., Vol. 54, 1948, pp. 416-421. Zbl0033.05201MR24963
  3. [3] P. Halmos, Measure Theory, Van Nostrand, Princeton, 1950. Zbl0040.16802MR33869
  4. [4] A. Liapunov, Sur les fonctions-vecteurs complètement additives, Bull. Acad. Sci. U.R.S.S., Ser. Math., Vol. 4, 1940, pp. 465-478 (Russian). Zbl0024.38504MR4080JFM66.0219.02
  5. [5] A. Liapunov, same as above, Vol. 10, 1946, pp. 277-279 (Russian); for an English version, see J. Diestel and J.J. Uhl, Vector Measures, 1977, A.M.S., Providence,Rhode Island, p. 262. 
  6. [6] J. Oxtoby, Measure and Category, Second Edition, Springer Verlag, New York, 1980. Zbl0435.28011MR584443
  7. [7] M. Valadier, Une mesure vectorielle sans atoms dont l'ensemble des valeurs est non convexe, Boll. U.M.I., Serie VI, Vol. II-C, No. 1, 1983, pp. 293-296. Zbl0523.28010MR718376

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