Title

Properties Of A Special Class Of Doubly Stochastic Measures

Keywords

AMS (1980) subject classification: Primary 28A35, 28A33, 60A10

Abstract

A measure μ on the unit square I } I is doubly stochastic if μ(A } I) = μ(I } A) = the Lebesgue measure of A for every Lebesgue measurable subset A of I = [0, 1]. By the hairpin L ∪L-1, we mean the union of the graphs of an increasing homeomorphism L on I and its inverse L-1. By the latticework hairpin generated by a sequence {xn:n ∈ Z} such that xn-1 < xn (n ∈ Z), {Mathematical expression}xn = 0 and {Mathematical expression}xn = 1, we mean the hairpin L ∪L-1, where L is linear on [xn-1, xn] and L(n) =xn-1 for n ∈ Z. In this note, a characterization of latticework hairpins which support doubly stochastic measures is given. This allows one to construct a variety of concrete examples of such measures. In particular, examples are given, disproving J. H. B. Kemperman's conjecture concerning a certain condition for the existence of doubly stochastic measures supported in hairpins. © 1988 Birkhäuser Verlag.

Publication Date

6-1-1988

Publication Title

Aequationes Mathematicae

Volume

36

Issue

2-3

Number of Pages

212-229

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF01836092

Socpus ID

34250094225 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34250094225

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