On the Lyapunov convexity theorem with appications to sign-embeddings
It is proved (Theorem 1) that for a Banach space $X$ the following assertions are equivalent:
(1) the range of every $X$- valued $σ$- additive nonatomic measure of finite variation possesses a convex closure;
(2) $L_1$ does not signembed in $X$.
English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1091-1098.
Citation Example: Kadets V. М., Popov M. M. On the Lyapunov convexity theorem with appications to sign-embeddings // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1192–1200.