Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Yet another proof of the Lyapunov convexity theorem


Author: Zvi Artstein
Journal: Proc. Amer. Math. Soc. 108 (1990), 89-91
MSC: Primary 28A12; Secondary 28A35
DOI: https://doi.org/10.1090/S0002-9939-1990-0993737-0
MathSciNet review: 993737
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new proof is given, of the convexity and compactness of the range of an atomless $ {R^n}$-valued measure.


References [Enhancements On Off] (What's this?)

  • [1] M. DeWilde, Sur un théoreme de Lyapounov, Bull. Soc. Roy. Sci. Liège 38 (1969), 96-100. MR 0245747 (39:7053)
  • [2] H. Halkin, Some further generalizations of a theorem of Lyapunov, Arch. Rational Mech. Anal. 17 (1964), 272-277. MR 0174421 (30:4625)
  • [3] P. R. Halmos, The range of a vector measure, Bull. Amer. Math. Soc. 54 (1948), 416-421. MR 0024963 (9:574h)
  • [4] S. Koshi, A remark on Lyapunov-Halmos-Blackwell convexity theorem, Math. J. Okayama Univ. 14 (1969), 29-33. MR 0265552 (42:461)
  • [5] A. A. Liapounoff, Sur les fonctions-vecteurs compètment additives, Izv. Akad. Nauk SSSR 4 (1940), 465-478. MR 0004080 (2:315e)
  • [6] J. Lindenstrauss, A short proof of Liapounoff's convexity theorem, J. Math. Mech. 15 (1966), 971-972. MR 0207941 (34:7754)
  • [7] C. Olech, The range of an unbounded vector valued measure, Math. Systems Theory 2 (1968), 251-256. MR 0239040 (39:399)
  • [8] J. A. Yorke, Another proof of Liapounov convexity theorem, SIAM J. Control. Optim. 9 (1971), 351-353. MR 0302263 (46:1416)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A12, 28A35

Retrieve articles in all journals with MSC: 28A12, 28A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0993737-0
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society