eBook - PDF

Classical and Modern Integration Theories

Name: Classical and Modern Integration Theories
ISBN: 9781483268699

Ivan N. Pesin,

Z. W. Birnbaum,

E. Lukacs,

218 pages
English
PDF
Available on iOS & Android

eBook - PDF

Classical and Modern Integration Theories

Ivan N. Pesin,

Z. W. Birnbaum,

E. Lukacs,

About this book

Classical and Modern Integration Theories discusses classical integration theory, particularly that part of the theory directly associated with the problems of area. The book reviews the history and the determination of primitive functions, beginning from Cauchy to Daniell. The text describes Cauchy's definition of an integral, Riemann's definition of the R-integral, the upper and lower Darboux integrals. The book also reviews the origin of the Lebesgue-Young integration theory, and Borel's postulates that define measures of sets. W.H. Young's work provides a construction of the integral equivalent to Lebesque's construction with a different generalization of integrals leading to different approaches in solutions. Young's investigations aim at generalizing the notion of length for arbitrary sets by means of a process which is more general than Borel's postulates. The text notes that the Lebesgue measure is the unique solution of the measure problem for the class of L-measurable sets. The book also describes further modifications made into the Lebesgue definition of the integral by Riesz, Pierpont, Denjoy, Borel, and Young. These modifications bring the Lebesgue definition of the integral closer to the Riemann or Darboux definitions, as well as to have it associated with the concepts of classical analysis. The book can benefit mathematicians, students, and professors in calculus or readers interested in the history of classical mathematics.

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Yes, you can access Classical and Modern Integration Theories by Ivan N. Pesin, Z. W. Birnbaum,E. Lukacs in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.