Explore the core concepts of measure theory in n-dimensional Euclidean space with ‘Measure Theory and Fine Properties of Functions, Second Edition’. This authoritative textbook delves into Hausdorff measure and capacity, crucial for understanding the fine properties of sets and functions. Ideal for mathematicians and graduate students, it covers essential topics like Besicovitch’s covering theorem, Rademacher’s theorem, area and coarea formulas, Sobolev and BV functions, sets of finite perimeter, and Aleksandrov’s theorem. This updated edition offers enhanced clarity, new material on subdifferentials of convex functions, and an updated bibliography. The book focuses on succinct, technical proofs, assuming a strong foundation in Lebesgue and abstract measure theory. Discover advanced mathematical analysis topics, rarely taught elsewhere, in this comprehensive guide from The Bookish Owl.