On integration with respect to a DT-measure

DT -measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space with respect to a DT -measure and investigate the following: multiplicativity of this integral, w ∗ -topology on the family of DT -measures and...

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Published in:	Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 20; no. 3; pp. 579 - 598
Main Author:	Svistula, Marina
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.09.2016 Springer Nature B.V
Subjects:	Calculus of Variations and Optimal Control; Optimization Econometrics Fourier Analysis Integration Mathematics Mathematics and Statistics Operator Theory Potential Theory Studies Topological manifolds Topology w-topology 28C05 Integration 28C15 Topological measure
ISSN:	1385-1292, 1572-9281
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Abstract	DT -measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space with respect to a DT -measure and investigate the following: multiplicativity of this integral, w ∗ -topology on the family of DT -measures and density of various subfamilies of this space, and also integral as a set function.
AbstractList	DT -measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space with respect to a DT -measure and investigate the following: multiplicativity of this integral, w ∗ -topology on the family of DT -measures and density of various subfamilies of this space, and also integral as a set function. DT-measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space with respect to a DT-measure and investigate the following: multiplicativity of this integral, - topology on the family of DT-measures and density of various subfamilies of this space, and also integral as a set function.
Author	Svistula, Marina
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Cites_doi	10.1090/S0002-9939-98-04494-3 10.1070/SM2013v204n05ABEH004318 10.1090/S0002-9947-97-01902-8 10.4064/fm174-3-4 10.1090/S0002-9947-06-03843-8 10.1007/BF01444904 10.1016/0001-8708(91)90035-6 10.1007/978-3-540-34514-5 10.4064/fm-147-3-213-237
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References	Butler (CR5) 2002; 174 Grubb, LaBerge (CR7) 1998; 126 Johansen, Rustad (CR8) 2006; 358 Aarnes (CR2) 1993; 295 Svistula (CR10) 2008; 62 CR4 Aarnes (CR1) 1991; 86 Aarnes (CR3) 1995; 147 Grubb (CR6) 1997; 349 Svistula (CR11) 2013; 204 Kelley (CR9) 1955 JF Aarnes (373_CR1) 1991; 86 JF Aarnes (373_CR2) 1993; 295 373_CR4 MG Svistula (373_CR11) 2013; 204 JF Aarnes (373_CR3) 1995; 147 SV Butler (373_CR5) 2002; 174 Ø Johansen (373_CR8) 2006; 358 MG Svistula (373_CR10) 2008; 62 DJ Grubb (373_CR7) 1998; 126 JL Kelley (373_CR9) 1955 DJ Grubb (373_CR6) 1997; 349
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Snippet	DT -measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space... DT-measures generalize the topological measures of Aarnes. We continue to study an integral of a real-valued continuous function on compact Hausdorff space...
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SubjectTerms	Calculus of Variations and Optimal Control; Optimization Econometrics Fourier Analysis Integration Mathematics Mathematics and Statistics Operator Theory Potential Theory Studies Topological manifolds Topology
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Title	On integration with respect to a DT-measure
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