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OverviewHenstock-Kurzweil (HK) integration, which is based on integral sums, can be obtained by an inconspicuous change in the definition of Riemann integration. It is an extension of Lebesgue integration and there exists an HK-integrable function f such that its absolute value [f] is not HK-integrable. In this text HK integration is treated only on compact one-dimensional intervals. The concept of convergent sequences is transferred to the set P of primitives of HK-integrable functions; these convergent sequences of functions from P are called E-convergent. The main results are: there exists a topology U on P such that (1) (P,U) is a topological vector space, (2) (P,U) is complete, and (3) every E-convergent sequence is convergent in (P,U). On the other hand, there is no topology U fulfilling (2),(3) and (P,U) being a locally convex space. Full Product DetailsAuthor: Jaroslav Kurzweil (Academy Of Sciences, Czech Republic)Publisher: World Scientific Publishing Co Pte Ltd Imprint: World Scientific Publishing Co Pte Ltd Volume: 7 Dimensions: Width: 15.80cm , Height: 1.30cm , Length: 23.00cm Weight: 0.331kg ISBN: 9789810242077ISBN 10: 9810242077 Pages: 144 Publication Date: 12 April 2000 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntegrable functions and their primitives; gauges and Borel measurability; convergence; an abstract setting; an abstract setting with D countable; locally convex topologies tolerant to Q-convergence; topological vector spaces tolerant to Q-convergence; P as a complete topological vector space; open problems.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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