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P-adic distribution : ウィキペディア英語版 | P-adic distribution
In mathematics, a p-adic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of ''p''-adic 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 integer-valued 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.
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