On affine selections of maps of spaces of probability measures (Q1173544)

The following theorem is proved: Let \(f: X\to Y\) be a null-soft mapping of a bicompact space \(X\) onto a bicompact space \(Y\). Then for every measure \(\mu\in P(X)\) there exists an affine selection \(s_ \mu: P(Y)\to P(X)\) of the map \(P(f)\) passing through the measure \(\mu\). The needed notions should be found in the references. The proof is based on a theorem of Shchepin about the transfinite decomposition of \(f\) and on the reduction of the problem to the projection map \(f\) of \(Y\times Q\) onto \(Y\) where \(Q\) is the Hilbert cube.