Coalescence of measures and f-rearrangements of a function

• Autores: Lucio R. Berrone
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 12, Nº 2, 1999, págs. 477-509
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper addresses the question of characterizing optimum values in the problem sup{n(E) : m(E)£C}, {1} where m and n are measures defined on a s-finite measurable space X. With this purpose, the f-rearrangement of a function g is introduced so as to formalize the idea of rearranging the level sets of the function g according to how these sets are arranged in a given function f. A characterization of optima of problem (1) is then obtained in terms of dn/dm-rearrangements, dn/dm being the Radon-Nikodym derivative of the measure n with respect to m. When X is a topological space and m, n are Borel measures, we say that n is coalescent with respect to m when, for every C>0, there exist connected optima solving problem (1). A general criterion for coalescence is given and some simple examples are discussed.