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Attila Losonczi

Publications and source records attributed to Attila Losonczi.

16 recordsLinked to original sources
arXiv2024

On infinite versions of the prisoner problem

We investigate some versions of the famous 100 prisoner problem for the infinite case, where there are infinitely many prisoners and infinitely many boxes with labels. In this case, many questions can be asked about the admissible steps of the prisoners, the constraints they have to follow and also about the releasing conditions. We will present and analyze many versions and cases. In the infinite case, the solutions and methods require mainly analysis rather than combinatorics.

math.GM↗
arXiv2024

Points accessible in average by rearrangement of sequences

We investigate the set of limit points of averages of rearrangements of a given sequence. We study how the properties of the sequence determine the structure of that set and what type of sets we can expect as the set of such accessible points.

math.CA↗
arXiv2024

The Hausdorff-integral on h-measure spaces and its applications

We are going to widen the scope of the previously defined Hausdorff-integral in two ways. First, in the sense, that we develop the theory of the integral on some naturally generalized measure spaces. Second, we extend it to functions taking values in $[0,+\infty)\times[0,+\infty)$. In all our intentions, we follow the same attitude that we had in our previous investigation, i.e. we work in the realm of Hausdorff dimension and measure.

math.CA↗
arXiv2024

The Hausdorff-integral and its applications

We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and its similarities to the properties of the Lebesgue integral. We present many applications as well.

math.CA↗
arXiv2023

Measures by means, means by measures

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 study the properties and behavior of such generalized means that are obtained by a measure, and we provide some applications as well.

math.CA↗
arXiv2021

Small perturbations on means and quasi-means

We start to investigate how small changes on the definition of ordinary means affect their properties. Especially the property of being a mean. In that direction we are looking for weakenings of the basic defining property of means. Hence we introduce weaker notions in two directions. We investigate such functions and provide many examples as well.

math.GM↗
arXiv2019

On the cardinality of $π(δ)$

We prove that the cardinality of transitive quasi-uniformities in a quasi-proximity class is at least $2^{2^{\aleph_0}}$ if there exist at least two transitive quasi-uniformities in the class. The transitive elements of $π(δ)$ are characterized if ${\cal V}_δ$ is transitive, and in this case we give a condition when there exists a unique transitive quasi-uniformity in $π(δ)$.

math.GN↗
arXiv2018

Extending means to several variables

We begin the study of how to extend few variable means to several variable ones and how to shrink means of several variables to less variables. With the help of one of the techniques we show that it is enough to check an inequality between two quasi-arithmetic means in 2-variables and that simply implies the inequality in m-variables. The technique has some relation to Markov chains. This method can be applied to symmetrization and compounding means as well.

math.CA↗
arXiv2018

Means of infinite sets III

We study various topics, e.g. accumulation points by a mean, two types of derivative by a mean, two new continuity and a boundedness concepts, we construct new means from old ones, finally we investigate the limit of means.

math.CA↗
arXiv2018

Means of infinite sets II

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 monotonicity and continuity because there is no single way to define such notions, instead there is a wide variety.

math.CA↗
arXiv2018

On mean-sets

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 means.

math.CA↗
arXiv2018

Means of infinite sets I

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 points, other deals with average using integral, other with limit of average on surroundings and one deals with evenly distributed samples. We study various properties of such means and their relations to each other.

math.CA↗
arXiv2018

Means of unbounded sets

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 extended to this type of mean. We generalize some classic means and also present many new examples for means defined on unbounded sets.

math.CA↗
arXiv2017

Dimension structures

We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.

math.CA↗
arXiv2017

Measuring sets by means

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 another way to compare subsets by a mean.

math.CA↗