HERGLOTZ-BOCHNER REPRESENTATION THEOREM VIA THEORY OF DISTRIBUTIONS
نویسندگان
چکیده
منابع مشابه
Nonstandard Proofs of Herglotz, Bochner and Bochner-Minlos Theorems
We describe a unified approach to Herglotz, Bochner and BochnerMinlos theorems using a combination of Daniell integral and nonstandard analysis. The proofs suggest a natural extension of the last two theorems to the case when the characteristic function is not continuous. This extension is proven and is demonstrated to be the best one possible. The goal of this paper is to show how the classic ...
متن کاملThe Bochner-Minlos theorem
If X is a topological space, and for m ≥ n the maps πm,n : X → X are defined by (πm,n(x))(j) = x(j), j ∈ {1, . . . , n}, then the spaces X and maps πm,n constitute a projective system, and its limit in the category of topological spaces is XN with the maps πn : X N → X, where XN has the initial topology for the family {πn : n ∈ N} (namely, the product topology). We say that a function f : XN → ...
متن کاملLusin’s Theorem and Bochner Integration
Abstract. It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover, every appropriate sum of this form will be within a preassigned ε of the integral, with the sum for the local errors also less than ε. All of this follows from the ubiquity of Lebesgue points, which is a co...
متن کاملBOCHNER - KÄHLER METRICS 3 Theorem
A Kähler metric is said to be Bochner-Kähler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least 2. In this article it will be shown that, in a certain well-defined sense, the space of Bochner-Kähler metrics in complex dimension n has real dimension n+1 and a recipe for an explicit formula for any Bochner-Kähler met...
متن کاملSkorohod Representation Theorem Via Disintegrations
Let (μn : n ≥ 0) be Borel probabilities on a metric space S such that μn → μ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn ∼ μn for all n and Xn → X0 in probability. By Skorohod’s theorem, Skorohod representation holds (with Xn → X0 almost uniformly) if μ0 is separable. Two results are proved in this paper. Fi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Operations Research Society of Japan
سال: 2017
ISSN: 0453-4514,2188-8299
DOI: 10.15807/jorsj.60.122