6 papers
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…
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…
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…