相关论文: Uniform measures and countably additive measures

An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…

A semigroup A is an abelian semigroup with identity 0. A set of positives in A is an ordered down-directed set P containing with every r an element r/2 with r/2 + r/2 = r. A continuity space is an abstract set X equipped with a map d : XxX…

Let $(X,\mathcal{B},\mu,T)$ be a measure preserving system. We say that a function $f\in L^2(X,\mu)$ is $\mu$-mean equicontinuous if for any $\epsilon>0$ there is $k\in \mathbb{N}$ and measurable sets ${A_1,A_2,\cdots,A_k}$ with…

Let u be a subharmonic function in D={|z|<1}. There exist an absolute constant C and an analytic function f in D such that \int_D |u(z)-log|f(z)|| dm(z)<C where m denotes the plane Lebesgue measure. We also consider uniform approximation.

The evolution of a measured system and an experimental apparatus is presented in an unified form. Conditions under which the state of such a total system forms, evaluates and declines from a superposition of states are defined. The problem…

Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…

In this article, we conduct a detailed study of \emph{finitely additive measures} (fams) in the context of Boolean algebras, focusing on three specific topics: freeness and approximation, existence and extension criteria, and integration…

In this paper, we introduced some notions on the n-Normed Spaces. Those are bounded k-linear (or multilinear) functionals and k-continuous (or multicontinuous) functions with k \in \mathbb{N}. We defined k-linear functionals under several…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

A function f:R -> R is approximately continuous iff it is continuous in the density topology, i.e., for any ordinary open set U the set E=f^{-1}(U) is measurable and has Lebesgue density one at each of its points. Denjoy proved that…

We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the…

It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…

We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded sequence of convex functions, we prove that the uniform…

Let $\mu$ be a self-similar measure satisfying the finite type condition. It is known that the set of attainable local dimensions for such a measure is a union of disjoint intervals, where some intervals may be degenerate points. Despite…

This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain…

We show how localization and smoothing techniques can be used to establish universality at the edge of the spectrum for a fixed positive measure on [-1,1]. Assume that the measure is a regular measure, and is absolutely continuous in some…

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the…

This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…

In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…