Regular Non-Additive Multimeasures. Fundaments and Applications

Contents
1 Introduction
	References
2 Types of Multimeasures
	References
3 Regular Multimeasures in the Hausdorff Metric Topology
	3.1 Basic Notions and Results
	3.2 Extensions of Regular Multimeasures
	3.3 Set-Valued Egoroff and Lusin Type Theorems
	3.4 Regular Non-atomic Multimeasures
	References
4 Regular Multimeasures in the Vietoris Topology
	4.1 Introduction
	4.2 Basic Notions and Results
	References
5 Approximation Theorems for Multimeasures in the Vietoris Topology
	5.1 Introduction
	5.2 Terminology, Basic Notions and Results
	5.3 Convergences in the Vietoris Topology
	5.4 Set-Valued Egoroff and Lusin Type Theorems in the Vietoris Topology
	5.5 Certain Physical Implications and Correlations
	5.6 Regularity of the Multimeasures in the Wijsman Topology
	References
6 Regularity and Atomicity in an Abstract Hypertopology for Multimeasures
	6.1 Introduction
	6.2 Basic Notions and Terminology
	6.3 Considerations on Non-atomicity and Regularity
	6.4 Regularity in Its Most General Sense
	References
7 Regularity of the Gould and Choquet Integrals
	7.1 Introduction
	7.2 Preliminaries
	7.3 Monotone Multimeasures (With Respect to an Arbitrary Order Relation)
	7.4 Gould Integrability
	7.5 Important Properties of the Gould Integral
	7.6 Certain Regularity Properties of the Gould and Choquet Interval-Valued Integrals
	References
Appendix A Multivalued Functions and Related Integrals
A.1 Introduction
A.2 Families of Subsets of Banach space
A.3 Measures
A.4 Fixed Point Theorems
A.5 Some Multivalued Additive Integrals
Appendix B Multimeasures and Integrals
B.1 Multimeasures
B.2 Integration with Respect to Multimeasures
Index