Open AccessOn Liapunov's convexity theorem.
Author(s) -
A Dvoretzky
Publication year - 1994
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.91.6.2145
Subject(s) - convexity , mathematics , liapunov function , mathematical economics , mathematical analysis , economics , physics , nonlinear system , financial economics , quantum mechanics
A necessary and sufficient condition is given for the range of a finite Rn-valued measure to be convex. A related result is given for Banach-valued set functions.