On Sazonov type topology inp-adic Banach space

Local fields, Gaussian measures, and Brownian motions

“…In contrast, there has not been a similarly extensive study of probability on local field objects. Most of the small body of work that we are aware of may be found in Karwowski, 1991, 1994], [Brillinger, 1991], [Evans, 1988a[Evans, , 1988b[Evans, , 1989a[Evans, , 1989b[Evans, , 1991[Evans, , 1993, [Guimier, 1989], [Madrecki, 1983[Madrecki, , 1985[Madrecki, , 1990[Madrecki, , 1991, and [Missarov, 1989[Missarov, , 1991. We should remark, however, that if one ignores the algebraic structure of local fields and thinks of them merely as ultrametric spaces or sets with a tree-like structure, then this work can be seen as part of the large and growing literature on probability in such a setting.…”

Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space

“…Proof is quite analogous to that of Lemma 4.4 [32] with substitution of P on P . (ii) and Proposition 3.1(2) [32] it follows, that f (x) is continuous in the norm topology.…”

“…Proof is quite analogous to that of Lemma 4.4 [32] with substitution of P on P . (ii) and Proposition 3.1(2) [32] it follows, that f (x) is continuous in the norm topology. From Chapters 7,9 [35] it follows, that there exists a consistent family of tight measures µ n on K n such thatμ n (x) = f n (x) for each x ∈ K n .…”

“…Therefore, Lemma 4.1 [32] is transferable onto the case of K s -valued measures, since Q ⊂ K s . Therefore, analogously to Equation (4.1) of Lemma 4.2 [32] we have…”

“…In this article measures are considered on Banach spaces, though the results given below can be developed for more general topological vector spaces, for example, it is possible to follow the ideas of works [29,30,31], in which were considered non-Archimedean analogs of the Minlos-Sazonov theorems for real-valued measures on topological vector spaces over non-Archimedean fields of zero characteristic. But it is impossible to make in one article.…”