ANALYSIS ON GAUSSIAN SPACES

The book explores the analysis of functions in finite-dimensional Euclidean spaces concerning the Lebesgue measure, highlighting its foundational role in mathematics. It addresses the complexities of extending these concepts to infinite dimensions, where the absence of Lebesgue measure presents challenges. The Gaussian measure emerges as the primary alternative in infinite-dimensional spaces, unified under the concept of "abstract Wiener space," providing a framework for understanding these advanced mathematical principles.