Elementary Introduction to the Lebesgue Integral

Description

It is important and useful to have a text on the Lebesgue theory that is accessible to bright undergraduates. This is such a text. Going back to the days of Isaac Newton and Gottfried Wilhelm von Leibniz, and even to Newton's teacher Isaac Barrow, the integral has been a mainstay of mathematical analysis. The integral is a device for amalgamating information. It is a powerful and irreplaceable tool. The text concentrates on the real line. The student will be familiar with the real numbers and will be comfortable internalizing the new ideas of measure theory in that context. In addition to having copious examples and numerous figures, this book includes a Table of Notation and a Glossary. Content: 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