Measure, Integration and Real Analysis

This textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, it lays the foundations for further study by promoting a deep understanding of key results.

Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.

Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.

Extensively class tested at multiple universities and written by an award-winning mathematical expositor, this book is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed;