5 citations · 5 across the 4 of their papers we have counts for
11 papers
Quasi-linear maps and image transformations
S. V. Butler
Conic quasi-linear maps are nonlinear operators from to a normed linear space which preserve nonnegative linear combinations on positive cones generated by single func…
Semisolid sets and topological measures
Svetlana V. Butler
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection…
Weak convergence of topological measures
Svetlana V. Butler
Topological measures and deficient topological measures are defined on open and closed subsets of a topological space, generalize regular Borel measures, and correspond to (non-lin…
Integration with respect to deficient topological measures on locally compact spaces
Svetlana V. Butler
Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient t…
Decompositions of signed deficient topological measures
Svetlana V. Butler
This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These…
Signed topological measures on locally compact spaces
Svetlana V. Butler
In this paper we define and study signed deficient topological measures and signed topological measures (which generalize signed measures) on locally compact spaces. We prove that…
Repeated quasi-integration on locally compact spaces
Svetlana V. Butler
When is locally compact, a quasi-integral (also called a quasi-linear functional) on is a homogeneous, positive functional that is only assumed to be linear on singly…
Non-linear functionals, deficient topological measures, and representation theorems on locally compact spaces
Svetlana V. Butler
We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topologica…
Quasi-linear functionals on locally compact spaces
Svetlana V. Butler
This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to…
Deficient topological measures on locally compact spaces
Svetlana V. Butler
Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A defici…
Solid-set functions and topological measures on locally compact spaces
Svetlana Butler
A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular o…