Integrable functions for the Bernoulli measures of rank 1
Annales mathématiques Blaise Pascal, Volume 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: 10.5802/ambp.287
Classification: 46S10
Keywords: integrable functions, Bernoulli measures of rank 1, invertible measures
Hamadoun Maïga 1

1 Département de Mathématiques et d’Informatique Faculté des Sciences et Techniques Université de Bamako Bamako Mali
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Hamadoun Maïga. Integrable functions for the Bernoulli measures of rank $1$. Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 2, pp. 341-356. doi : 10.5802/ambp.287. https://ambp.centre-mersenne.org/articles/10.5802/ambp.287/

[1] Bertin Diarra Base de Mahler et autres, Séminaire d’Analyse, 1994–1995 (Aubière) (Sémin. Anal. Univ. Blaise Pascal (Clermont II)), Volume 10, Univ. Blaise Pascal (Clermont II), Clermont-Ferrand, 1997, pp. Exp. No. 16, 18 | MR | Zbl

[2] Bertin Diarra Cours d’analyse p-adique (1999 - 2000) (Technical report)

[3] Neal Koblitz p-adic Numbers, p-adic Analysis and Zeta-Functions, Springer-Verlag, New York - Heidelberg - Berlin, 1977 | MR | Zbl

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

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

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

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

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