4 citations · 15 across the 13 of their papers we have counts for
13 papers
Small perturbations on means and quasi-means
Attila Losonczi
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…
A common generalization of infinite sum, unordered sum and integral
Attila Losonczi
We present a common ground for infinite sums, unordered sums, Riemann/Lebesgue integrals, arc length and some generalized means. It is based on extending functions on finite sets u…
On the cardinality of
Attila Losonczi
We prove that the cardinality of transitive quasi-uniformities in a quasi-proximity class is at least if there exist at least two transitive quasi-uniformities i…
Points accessible in average by rearrangement of sequences
Attila Losonczi
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 t…
Means of infinite sets III
Attila Losonczi
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,…
On mean-sets
Attila Losonczi
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.…
Means of unbounded sets
Attila Losonczi
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…
Dimension structures
Attila Losonczi
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 pro…
Measuring sets by means
Attila Losonczi
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…
Measures by means, means by measures
Attila Losonczi
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 geome…
Means of infinite sets II
Attila Losonczi
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 c…
Means of infinite sets I
Attila Losonczi
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 ideal…
Extending means to several variables
Attila Losonczi
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 techniqu…