Integrable functions for the Bernoulli measures of rank 1
Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 2, p. 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
Keywords: integrable functions, Bernoulli measures of rank 1, invertible measures
@article{AMBP_2010__17_2_341_0,
     author = {Ma\"\i ga, Hamadoun},
     title = {Integrable functions for the Bernoulli measures of rank $1$},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {17},
     number = {2},
     year = {2010},
     pages = {341-356},
     doi = {10.5802/ambp.287},
     mrnumber = {2778916},
     zbl = {1207.26031},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2010__17_2_341_0}
}
Maïga, Hamadoun. 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. http://www.numdam.org/item/AMBP_2010__17_2_341_0/

[1] Diarra, Bertin Base de Mahler et autres, Séminaire d’Analyse, 1994–1995 (Aubière), Univ. Blaise Pascal (Clermont II), Clermont-Ferrand (Sémin. Anal. Univ. Blaise Pascal (Clermont II)) Tome 10 (1997), pp. Exp. No. 16, 18 | MR 1461327 | Zbl 0999.12014

[2] Diarra, Bertin Cours d’analyse p-adique, Université de Bamako, Faculté des Sciences et Techniques (1999 - 2000) (Technical report)

[3] Koblitz, Neal p-adic Numbers, p-adic Analysis and Zeta-Functions, Springer-Verlag, New York - Heidelberg - Berlin (1977) | MR 466081 | Zbl 0364.12015

[4] Monna, A. F.; Springer, T. A. Intégration non-archimédienne. I, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math., Tome 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., Tome 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