Measure And Integration: An Advanced Course In Basic Procedures And Applications

This book aims at restructuring some fundamentals in measure and integration theory and thus to free the theory from notorious drawbacks. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond. Thus it extends the Riesz representation theorem in terms of Radon measures from locally compact to arbitrary Hausdorff topological spaces.