padic distribution

In mathematics, a padic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of padic numbers.
Definition
If X is a topological space, a distribution on X with values in an abelian group G is a finitely additive function from the compact open subsets of X to G. Equivalently, if we define the space of test functions to be the locally constant and compactly supported integervalued functions, then a distribution is an additive map from test functions to G. This is formally similar to the usual definition of distributions, which are continuous linear maps from a space of test functions on a manifold to the real numbers.
padic measures
A padic measure is a special case of a padic distribution, analogous to a measure on a measurable space. A padic distribution taking values in a normed space is called a padic measure if the values on compact open subsets are bounded.
References
 Colmez, Pierre (2004), Fontaine's rings and padic Lfunctions, http://www.math.jussieu.fr/~colmez/tsinghua.pdf
 Koblitz, Neal (1984), padic Numbers, padic Analysis, and ZetaFunctions, Graduate Texts in Mathematics, vol. 58, Berlin, New York: SpringerVerlag, ISBN 9780387960173, MR754003
 Mazur, Barry; SwinnertonDyer, P. (1974), "Arithmetic of Weil curves", Inventiones Mathematicae 25: 1–61, doi:10.1007/BF01389997, ISSN 00209910, MR0354674
 Washington, Lawrence C. (1997), Cyclotomic fields (2nd ed.), Berlin, New York: SpringerVerlag, ISBN 9780387947624
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