The Lebesgue-Stieltjes Integral A Practical Introduction [Paperback]

While mathematics students generally meet the Riemann integral early in their undergraduate studies, those whose interests lie more in the direction of applied mathematics will probably find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral before they have acquired the necessary theoretical background. This book is aimed at exactly this group of readers. The authors introduce the Lebesgue-Stieltjes integral on the real line as a natural extension of the Riemann integral, making the treatment as practical as possible. They discuss the evaluation of Lebesgue-Stieltjes integrals in detail, as well as the standard convergence theorems, and conclude with a brief discussion of multivariate integrals and surveys of L spaces plus some applications. The whole is rounded off with exercises that extend and illustrate the theory, as well as providing practice in the techniques.Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at 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 Lebesgue 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 natural way as an extension of the Riemann integral. They have tried to make 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 ok L^p spaces and some applications. Exercises, which extend and illustrate the theory, and provide practice in techniques, are included. Michalc¨