Measure and Integration

This book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom. Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text. Hints are included for some of the more difficult problems.

Axiomatic treatment of Lebesgue integration allows quick access to the main convergence of theorems Includes a brief introduction to Fourier analysis in the Euclidean setting Provides a treatment of standard measure spaces and analytic sets Detailed index provides easy navigation to the main results Includes supplementary material: sn.pub/extras

Autorentext
Hari Bercovici is a Professor in the Department of Mathematics at Indiana University Bloomington. His research interests include functional analysis, operator theory, and free probability.
Carl Pearcy is an Emeritus Professor in Mathematics at Texas A&M University. His research interest is in functional analysis.

Inhalt
Rings of sets.- Measurability.- Integrals and Measures.- Convergence Theorems for Lebesgue Integrals.- Existence and Uniqueness of Measures.- Signed Measures, Complex Measures and Absolute Continuity.- Measure and Topology.- Product Measures.- The Lp Spaces.- Fourier Analysis.- Standard Measure Spaces.