Measure and Integration

Focusing on the restructuring of measure and integration theory, this book addresses limitations of traditional tools like the Carathéodory and Daniell-Stone theorems. It introduces a new systematic approach based on regularity, linking it to topology, and thereby unifying various concepts within measure theory. The text extends the Riesz representation theorem to arbitrary Hausdorff spaces and integrates non-additive set functions, enhancing the Choquet capacitability theorem. Designed for researchers and educators, the book is self-contained and accessible from foundational concepts.