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
potential applications in life sciences, are opened.