6 papers · 2 filters
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…