The Lebesgue-Stieltjes Integral. - A Practical Introduction (Relié)

B Van Brunt, M Carter

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  • Springer

  • Paru le : 12/07/2000
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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.
    • Real numbers
    • Some analytic preliminaries
    • The Riemann integral
    • The Lebesgue-Stieltjes integral
    • Properties of the integral
    • Integral calculus
    • Double and repeated integrals
    • The Lebesgue spaces Lp
    • Hilbert spaces and L²
  • Date de parution : 12/07/2000
  • Editeur : Springer
  • Collection : undergraduate texts in maths
  • ISBN : 0-387-95012-5
  • EAN : 9780387950129
  • Présentation : Relié
  • Nb. de pages : 228 pages
  • Poids : 0.495 Kg
  • Dimensions : 16,0 cm × 24,2 cm × 1,6 cm
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 include applications of the Henstock integral to ordinary and partial differential equations.

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B Van Brunt et M Carter - The Lebesgue-Stieltjes Integral. - A Practical Introduction.
The Lebesgue-Stieltjes Integral.. A Practical Introduction
64,15 €
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