Atomicity through Fractal Measure Theory Mathematical and Physical Fundamentals with Applications /

• Main Authors: Gavriluţ, Alina (Author, http://id.loc.gov/vocabulary/relators/aut), Mercheş, Ioan (http://id.loc.gov/vocabulary/relators/aut), Agop, Maricel (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Subjects: Measure theory.; Quantum physics.; Mathematical physics.; Measure and Integration.; Quantum Physics.; Mathematical Applications in the Physical Sciences.

This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through...

Table of Contents:

• Preface
• 1. Short hypertopologies. A short overview
• 2. A Mathematical-physical approach on regularity in hit-and-miss hypertologies for fuzzy set multifunctions
• 3. Non-atomic set multifunctions
• 4. Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions
• 5. Atoms and pseudo-atoms for set multifunctions
• 6. Gould integrability on atoms for set multifunctions
• 7. Continuity properties and the Alexandroff theorem in Vietoris topology
• 8. Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity- 9. Atomicity via regularity for non-additive set malfunctions
• 10. Extended atomicity through non-differentiability and its physical implications
• 11. On a multifractal theory of motion in a non-differentiable space. Toward a possible multifractal theory of measure
• List of symbols
• Index.