Some negative results on existence of Sazonov topology inl-adic Frechet spaces

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.…”

“…We remark that essentially the same class of measures that we are led to was derived in [Madrecki, 1983] from different considerations. (As far as we can ascertain, this paper has not been published, but some of its essence can be gleaned from [Madrecki, 1985[Madrecki, , 1990[Madrecki, , 1991. )…”

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

“…Lemmas 1, 2 and corollary 1 §23 [38] may be transferred on a Banach space X over K. Let us take h ξ (x) = Hn h(x + y)γ ξ,n (x)m Hn (dx), where γ ξ,n corresponds to H n and m Hn are the same as in §2. 30. Choosing |ξ l | → ∞ whilst l → ∞ as in Lemma 3 §23[38] we get the statement of Lemma 3.15.…”

“…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.…”