相关论文: On additive property of finitely additive measures

We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.

We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural…

Let $L$ be a linear space of real bounded random variables on the probability space $(\Omega,\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\mathcal{A}$, such that $P\sim P_0$ and $E_P(X)=0$ for all $X\in L$, if and…

The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…

We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.

We investigate some properties of density measures -- finitely additive measures on the set of natural numbers $\N$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the…

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…

We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp…

An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…

We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.

Given an infinite group G, we consider the finitely additive measure defined on finite unions of cosets of finite index subgroups. We show that this shares many properties with the size of subsets of a finite group, for instance we can…

This lecture notes are intended for the students taking courses in mathematical control theory. They are concerned with the attainability problem with constraints. The exposition is oriented to the linear control problems with the impulse…

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…

We prove in particular that the Lipschitz-free space over a finitely-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective projection is $1$. As a tool to obtain the main result we establish…

We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…

We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set.

The Baire category theorem states that every complete pseudometric space is a Baire space. There are some results in metric spaces which have their analogue in uniform spaces, however this is not one of them. Nonetheless, since the Baire…

A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures…

The concept of additive basis has been investigated in the literature for several mathematicians which works with number theorem. Recently, the concept of finitely stable additive basis was introduced. In this note we provide a…

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…