A radon nikodym theorem in the non-archimedean setting
DOI:
https://doi.org/10.4067/S0716-09172001000300001Abstract
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.
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).
[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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