A radon nikodym theorem in the non-archimedean setting

• Moraga, Mirta ^[1] ; Aguayo, José ^[2]
  1. [1] Universidad de Magallanes

     Universidad de Magallanes

     Punta Arenas, Chile

     
  2. [2] Universidad de Concepción

     Universidad de Concepción

     Comuna de Concepción, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 20, Nº. 3, 2001, págs. 263-279
• Idioma: inglés
• DOI: 10.4067/S0716-09172001000300001
• Enlaces
  • Texto completo
• Resumen

  • In this paper we define the absolutely continuous relation between nonarchimedean scalar measures and then we give and prove a version of the Radon-Nykodym Theorem in this setting.We also define the nonarchimedean vector measure and prove some results in order to prepare a version of this Theorem in a vector case.

• Referencias bibliográficas
  • Citas [1] Aguayo, J., Non-Archimedean Integral Operators, Proyecto Fondecyt No. 1990341 and DIUC No. 98015013-1.0 of the University of Concepción,...
  • [2] Aguayo, J., De Grande de Kimpe, N. and Navarro, S. Strict Topology and Duals in Spaces of Function, (1997).
  • [3] Aguayo, J., De Grande de Kimpe, N., and Navarro, S. Strict Locally Convex Topologies on BC(X;IK), P-adic Functional Analysis, Proceedings...
  • [4] Aguayo, J., De Grande de Kimpe, N., and Navarro, S. Zero-Dimensional Pseudocompact and Ultraparacompact Spaces, P-adic Functional Analysis,...
  • [5] Aguayo, J. and Gilsdorf, T., Non-Archimedean vector measures and integral operator, 1999, preprint
  • [6] Monna, A. F. and Springer, T. A., Integration NonArchimedienne, Indag. Math., 25, N 4, pp. 634-653, (1968).
  • [7] Diestel, J. and Uhl, J., Vector Measures, Copyright by the American Mathematical Society, Mathematical Surveys, N 15, (1977).
  • [8] Prolla, J. B., Topics in Functional Analysis over Valued Division Rings, North Holland, Amsterdam, (1977).
  • [9] A. C. M. van Rooij, Non-Archimidean Functional Analysis, Marcel Dekker, Inc., (1978).
  • [10] A. C. M. van Rooij and W. H. Schikhof, Non-Archimidean Integration Theory,
  • [11] Schikhof, W: H., A Radon-Nikodym Theorem for NonArchimedean Integrals and Absolutely Continuous Measures on Groups, Koninkl. Nederl....
  • [12] Wheeden, R. L. and Zygmund, A., Measure and integral, New York, Marcel-Dekker, (1977).