Doubly stochastic measures with hairpin support. (English) Zbl 0629.60002

T. L. Seethoff and R. C. Shiflett [Z. Wahrscheinlichkeitstheor. Verw. Geb. 41, 283-288 (1978; Zbl 0364.60019)] proved nice uniqueness theorems concerning doubly stochastic measures supported on the union of the graphs of two functions, but the existence theorems were more elusive. In this present paper, using a functional equations approach, not only uniqueness results but also existence theorems are obtained for doubly stochastic measures with support sets of the form \(g\cup g^{-1}\) where g is an increasing homeomorphism of [0,1] onto itself such that \(g(x)<x\) whenever \(0<x<1\).


60A10 Probabilistic measure theory
28A35 Measures and integrals in product spaces
28A33 Spaces of measures, convergence of measures


Zbl 0364.60019
Full Text: DOI


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