Vol. 99, No. 2, 1982

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Counter-examples to some conjectures about doubly stochastic measures

Viktor Losert

Vol. 99 (1982), No. 2, 387–397
Abstract

Some new types of doubly stochastic measures are constructed. Using measure preserving transformations, one can construct examples of nontrivial extreme doubly stochastic measures which are absolutely continuous with respect to another extreme doubly stochastic measure (disproving a conjecture by Feldman). By combinatorial arguments, one gets an extreme doubly stochastic measure that is not concentrated on a countable union of function graphs and whose support is the whole unit square.

Mathematical Subject Classification 2000
Primary: 28A35
Secondary: 60A10, 60J99
Milestones
Received: 13 January 1981
Revised: 21 May 1981
Published: 1 April 1982
Authors
Viktor Losert