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

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.