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Atomicity through Fractal Measure Theory

Mathematical and Physical Fundamentals with Applications

Maricel Agop, Alina Gavriluţ, Ioan Mercheş, et al.

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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Analysis

Beschreibung

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 key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems.

The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potentialapplications in life sciences, are opened.

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Schlagwörter

non additive measure, nonlinear dynamics, quantum measure theory, fractality, fuzzy set multifunctions, multifractal theory, multivalued analysis, hypertopologies, atom, Alexandroff theorem, Gould integrability, pseudo atom, fractal measure theory, nonatomicity, non-atomic set multifunctions, Vietoris topology, atomicity