Table of Contents

*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Chapter I. Some Theorems on Real-valued Functions, pg. 1*Chapter II. The Lebesgue Integral, pg. 52*Chapter III. Measurable Sets and Measurable Functions, pg. 101*Chapter IV. The Integral as a Function of Sets; Convergence Theorems, pg. 136*Chapter V. Differentiation, pg. 188*Chapter VI. Continuity Properties of Measurable Functions, pg. 218*Chapter VII. The Lebesgue-Stieltjes Integral, pg. 242*Chapter VIII. The Perron Integral, pg. 312*Chapter IX. Differential Equations, pg. 336*Chapter X. Differentiation of Multiple Integrals, pg. 366*Appendix, pg. 383*Index, pg. 387