Full paper in PDF:
$%L. R. Berrone,
Coalescence of measures and f-rearrangements of a function, Rev. Mat. Complut. 12 (1999),
no. 2, 477–509.
%$
ABSTRACT
This paper addresses the question of characterizing optimum values in the problem
| (1) |
where and are measures defined on a -finite measurable space . With this purpose, the -rearrangement of a function is introduced so as to formalize the idea of rearranging the level sets of the function according to how these sets are arranged in a given function . A characterization of optima of problem (1) is then obtained in terms of -rearrangements, being the Radon-Nikodým derivative of the measure with respect to . When is a topological space and , are Borel measures, we say that is coalescent with respect to when, for every , there exist connected optima solving problem (1). A general criterion for coalescence is given and some simple examples are discussed.
1991 Mathematics Subject Classification: 49N99, 28A25, 26D10.