2019
Том 71
№ 11

All Issues

Kadets V. М.

Articles: 1
Article (English)

On the Lyapunov convexity theorem with appications to sign-embeddings

Kadets V. М., Popov M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1192–1200

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 $X$.