Positive additive functions with respect to interval filling sequences and some sequences of integers with gap conditions

1992 ◽  
Vol 31 (1) ◽  
pp. 42-52
Author(s):  
Z. Dar�czy ◽  
I. K�tai
Keyword(s):  
Additive Functions ◽  
Interval Filling

On completely additive functions related to interval-filling sequences

1990 ◽  
Vol 54 (2) ◽  
pp. 173-179 ◽  
Author(s):  
Z. Dar�czy ◽  
I. K�tai ◽  
T. Szab�
Keyword(s):  
Additive Functions ◽  
Interval Filling

scholarly journals On $p$ and $q$-Additive Functions

1999 ◽  
Vol 22 (1) ◽  
pp. 83-97 ◽  
Author(s):  
Yoshihisa UCHIDA
Keyword(s):  
Additive Functions

scholarly journals A Lebesgue decomposition for elements in a topological group

1980 ◽  
Vol 3 (4) ◽  
pp. 801-808
Author(s):  
Thomas P. Dence
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Projection Operators ◽  
Additive Functions ◽  
Lebesgue Decomposition ◽  
Algebra Of Sets

Our aim is to establish the Lebesgue decomposition for strongly-bounded elements in a topological group. In 1963 Richard Darst established a result giving the Lebesgue decomposition of strongly-bounded elements in a normed Abelian group with respect to an algebra of projection operators. Consequently, one can establish the decomposition of strongly-bounded additive functions defined on an algebra of sets. Analagous results follow for lattices of sets. Generalizing some of the techniques yield decompositions for elements in a topological group.

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