Wolfgang Filter Book order

The book explores the unification of two branches of integration theory: the abstract approach favored by probabilists and the topological approach preferred by analysts. It addresses the limitations of each theory when applied to complex spaces, proposing new definitions that reconcile these approaches. The integral introduced aligns with conventional definitions for Radon measures on Hausdorff spaces while offering broader applicability. This innovative framework aims to resolve the longstanding divide between the two theories, enhancing their collective utility.

The book presents material from an introductory integration theory course at ETH Zurich, tailored for third and fourth-year mathematics students. It balances accessibility and depth, focusing on essential concepts while providing a glossary for additional clarity. Readers should be familiar with the Riemann integral and basic point-set topology, particularly for advanced topics like 'Measures on Hausdorff Spaces.' The approach aims to cater to a broader audience, allowing those with limited prior knowledge to engage with the subject at an intermediate level.