Mass transport problem and derivation. (English) Zbl 0998.60012
Summary: A characterization of the transport property is given. New properties for strongly nonatomic probabilities are established. We study the relationship between the nondifferentiability of a real function \(f\) and the fact that the probability measure \(\lambda_{f^*}:=\lambda\circ (f^*)^{-1}\), where \(f^*(x):=(x,f(x))\) and \(\lambda\) is the Lebesgue measure, has the transport property.
MSC:
60E05 | Probability distributions: general theory |
26A27 | Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives |