Integrable functions for the Bernoulli measures of rank 1
Annales Mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 341-356.

In this paper, following the p-adic integration theory worked out by A. F. Monna and T. A. Springer [4, 5] and generalized by A. C. M. van Rooij and W. H. Schikhof [6, 7] for the spaces which are not σ-compacts, we study the class of integrable p-adic functions with respect to Bernoulli measures of rank 1. Among these measures, we characterize those which are invertible and we give their inverse in the form of series.

DOI : https://doi.org/10.5802/ambp.287
Classification : 46S10
Mots clés : integrable functions, Bernoulli measures of rank 1, invertible measures
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Maïga, Hamadoun. Integrable functions for the Bernoulli measures of rank $1$. Annales Mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 341-356. doi : 10.5802/ambp.287. http://www.numdam.org/articles/10.5802/ambp.287/

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[4] Monna, A. F.; Springer, T. A. Intégration non-archimédienne. I, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math., Volume 25 (1963), pp. 634-642 | MR 156936 | Zbl 0147.11803

[5] Monna, A. F.; Springer, T. A. Intégration non-archimédienne. II, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math., Volume 25 (1963), pp. 643-653 | MR 156937 | Zbl 0147.11803

[6] van Rooij, Arnoud C. M. Non-Archimedean Functional Analysis, M. Dekker, New York and Basel, 1978 | MR 512894 | Zbl 0396.46061

[7] Schikhof, Wilhelmus H. Ultrametric calculus - An introduction to p-adic analysis, Cambridge University Press, Cambridge, 1984 | MR 791759 | Zbl 0553.26006

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