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Elementary Introduction to the Lebesgue Integral Textbooks in Mathematics Series

Langue : Anglais

Auteur :

Couverture de l’ouvrage Elementary Introduction to the Lebesgue Integral

Elementary Introduction to the Lebesgue Integral is not just an excellent primer of the Lebesgue integral for undergraduate students but a valuable tool for tomorrow?s mathematicians. Since the early twentieth century, the Lebesgue integral has been a mainstay of mathematical analysis because of its important properties with respect to limits. For this reason, it is vital that mathematical students properly understand the complexities of the Lebesgue integral. However, most texts about the subject are geared towards graduate students, which makes it a challenge for instructors to properly teach and for less advanced students to learn.

Ensuring that the subject is accessible for all readers, the author presents the text in a clear and concrete manner which allows readers to focus on the real line. This is important because Lebesgue integral can be challenging to understand when compared to more widely used integrals like the Riemann integral. The author also includes in the textbook abundant examples and exercises to help explain the topic. Other topics explored in greater detail are abstract measure spaces and product measures, which are treated concretely.

Features:

  • Comprehensibly written introduction to the Lebesgue integral for undergraduate students

  • Includes many examples, figures and exercises

  • Features a Table of Notation and Glossary to aid readers

  • Solutions to selected exercises

Introductory Thoughts.The Purpose of Measures.The Lebesgue Integral.Integrable Functions.The Lebesgue Spaces. The Concept of Outer Measure.What is a Measurable Set? Decomposition Theorems.Creation of Measures. Instances of Measurable Sets. Approximation by Open and Closed Sets. Different Methods of Convergence. Measure on a Product Space. Additivity for Outer Measure. Nonmeasurable and Non-Borel Sets

Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 65 books and more than 175 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.