Related papers: Means of infinite sets III
We open a new field on how one can define means on infinite sets. We investigate many different ways on how such means can be constructed. One method is based on sequences of ideals, other deals with accumulation points, one uses isolated…
We continue the study of how one can define means of infinite sets. We introduce many new properties, investigate their relations to each other and how they can typify a mean. We collect the properties in property groups e.g. for…
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
I define three "measures" of the complicatedness of a finite group in terms of bases in permutation representations of the group, and consider their relationships to other measures.
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
We explain how the current knowledge on the set of complete noncompact constant mean curvature surfaces can be exploited to produce new examples of compact constant mean curvature surfaces of genus greater than or equal to 3.
For abelian length categories the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one…