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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 book HK integration is treated only on compact one-dimensional intervals.The set of convergent sequences of HK-integrable functions is singled out by an elementary convergence theorem. 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: 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 KurzweilPublisher: World Scientific Publishing Company Imprint: World Scientific Publishing Company ISBN: 9781299615199ISBN 10: 1299615198 Pages: 146 Publication Date: 01 January 2000 Audience: General/trade , General Format: Electronic book text Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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