Advanced Integration Theory

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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.