Lebesgue integration / Soo Bong Chae.

Includes bibliographical references (pages [249]-253) and index.

-- Ch. 0. Preliminaries. 1. Sets. 2. Relations. 3. Countable Sets. 4. Real Numbers. 5. Topological Concepts in R. 6. Continuous Functions. 7. Metric Spaces -- Ch. I. The Riemann Integral. 1. The Cauchy Integral. 2. Fourier Series and Dirichlet's Conditions. 3. The Riemann Integral. 4. Sets of Measure Zero. 5. Existence of the Riemann Integral. 6. Deficiencies of the Riemann Integral -- Ch. II. The Lebesgue Integral: Riesz Method. 1. Step Functions and Their Integrals. 2. Two Fundamental Lemmas. 3. The Class L[superscript +]. 4. The Lebesgue Integral. 5. The Beppo Levi Theorem -- Monotone Convergence Theorem. 6. The Lebesgue Theorem -- Dominated Convergence Theorem. 7. The Space L[superscript +] -- Ch. III. Lebesgue Measure. 1. Measurable Functions. 2. Lebesgue Measure. 3. [sigma]-Algebras and Borel Sets. 4. Nonmeasurable Sets. 5. Structure of Measurable Sets. 6. More About Measurable Functions. 7. Egoroff's Theorem. 8. Steinhaus' Theorem. 9. The Cauchy Functional Equation.