A radon nikodym theorem in the non-archimedean setting

Authors

  • Mirta Moraga Universidad de Magallanes.
  • José Aguayo Universidad de Concepción.

DOI:

https://doi.org/10.4067/S0716-09172001000300001

Abstract

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.

Author Biographies

Mirta Moraga, Universidad de Magallanes.

Departamento de Matemática y Fíisica, Facultad de Ciencia.

José Aguayo, Universidad de Concepción.

Departamento de Matemáticas, Facultad de Ciencias Físicas y Matemáticas.

References

[1] Aguayo, J., Non-Archimedean Integral Operators, Proyecto Fondecyt No. 1990341 and DIUC No. 98015013-1.0 of the University of Concepción, (1998).

[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 of the Fourth International Conference, Nijmegen, Netherlands, 1996

[4] Aguayo, J., De Grande de Kimpe, N., and Navarro, S. Zero-Dimensional Pseudocompact and Ultraparacompact Spaces, P-adic Functional Analysis, Proceedings of the Fourth International Conference, Nijmegen, Netherlands, (1996).

[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. Akademie Van WetenschappenAmsterdam, Reprinted from Proceedings, Series A, 74, N 1 and Indag. Math., 33, N 1, (1971).

[12] Wheeden, R. L. and Zygmund, A., Measure and integral, New York, Marcel-Dekker, (1977).

Published

2017-04-24

How to Cite

[1]
M. Moraga and J. Aguayo, “A radon nikodym theorem in the non-archimedean setting”, Proyecciones (Antofagasta, On line), vol. 20, no. 3, pp. 263-279, Apr. 2017.

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