Classical and Modern Integration Theories is popular PDF and ePub book, written by Ivan N. Pesin in 2014-07-03, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Classical and Modern Integration Theories can be Read Online from any device for your convenience.
Classical and Modern Integration Theories Book PDF Summary
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.
Detail Book of Classical and Modern Integration Theories PDF
- Author : Ivan N. Pesin
- Release : 03 July 2014
- Publisher : Academic Press
- ISBN : 9781483268699
- Genre : Mathematics
- Total Page : 218 pages
- Language : English
- PDF File Size : 18,9 Mb
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