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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 DEGREESp spaces and some applications.
Exercises, which extend and illustrate the theory, and provide
practice in techniques, are included. Michael Carter and Bruce van
Brunt are senior lecturers in mathematics at Massey University,
Palmerston North, New Zealand. Michael Carter obtained his Ph.D. at
Massey University in 1976. He has research interests in control
theory and differential equations, and has many years of experience
in teaching analysis. Bruce van Brunt obtained his D.Phil. at the
University of Oxford in 1989. His research interests include
differential geometry, differential equations, and analysis. His
publications
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.
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