Lectures on Measure and Integration

These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts.
Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

Harold Widom is Professor Emeritus of Mathematics at the University of California, Santa Cruz. His other Dover book is Lectures on Integral Equations.

I. MeasuresII. IntegrationIII. The Theorems of FubiniIV. Representations of MeasuresV. The Lebesgue SpacesVI. DifferentiationVII. Fourier Series