Lectures on Measure and Integration (Dover Books on Mathematics) by Harold Widom (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Why books as good as this one, risk to disappear forever?It is a tiny set of lecture notes, dealing with sigma algebras, measures and the integration process associated. It’s quite thin, but much detailed, covering Fubini and Radon-Nykodim theorems (no Riesz representation though). The geometric side of measure theory is limited to differentiation of measures. The book ends with a brief chapter on Fourier series. It compares well with later bigger introductions like Rudin’s

⭐first chapters or Aliprantis’

⭐. No exercises, but who need them? Great writing.

⭐Husband is in love.

⭐Conciso, porém completo. E muito preciso. Serve tanto num primeiro contato com a teoria de medida e integração, quanto para revisar o assunto. Único ponto contra é a inexistência de exercícios, mas dada a importância do assunto, é fácil encontrar exercícios pela internet.

⭐

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