The Lebesgue-Stieltjes Integral.. A Practical Introduction

Mathematics students generally are introduced to the Riemann integral early in their undergraduate studios; then at the advanced undergraduate or graduate level they receive a course on measure and integration dealing with the Lebesgue theory. However, those whose interests lie more in the direction of applied mathematics, will in all probability find themselves needing to use the Lebosgue or Lebesgue-Stieltjes integral without having the necessary theoretical background. It is to such readers that this book is addressed. The authors aim to introduce the Lebesgue-Stieltjes integral on the real line in a neural way as an extension of the Riemann integral. They made the treatment as practical as possible. The evaluation of Lebesgue- Stieltjes integrals is discussed in detail, as are the key theorems of integral calculus as well as the standard convergence theorems. The book then concludes with a brief discussion of multivariate integrals and surveys of Lp spaces and some applications. Exorcises, which extend and illustrate the theory, and provide practice in techniques, are included.