Given a continuous map s ↦ μs, from a compact metric space into the space of nonatomic measures on T, we show the existence of a family (Aα s)α∈[0,1], increasing in α and continuous in s, such that μs(Aα s)=αμs(T)(α∈[0,1]
Cellina, A., Colombo, G., Fonda, A. (1988). A continuous version of Liapunov's convexity theorem. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 5(1), 23-36 [10.1016/S0294-1449(16)30353-5].
A continuous version of Liapunov's convexity theorem
CELLINA, ARRIGO;
1988
Abstract
Given a continuous map s ↦ μs, from a compact metric space into the space of nonatomic measures on T, we show the existence of a family (Aα s)α∈[0,1], increasing in α and continuous in s, such that μs(Aα s)=αμs(T)(α∈[0,1]
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