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Henstock-Kurzweil Integration: Its Relation to Topological Vector Spaces (Real Analysis) [Hardcover]

By Jaroslav Kurzweil (Author)
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Item description for Henstock-Kurzweil Integration: Its Relation to Topological Vector Spaces (Real Analysis) by Jaroslav Kurzweil...

Henstock-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.



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Item Specifications...


Studio: World Scientific Publishing Company
Pages   136
Est. Packaging Dimensions:   Length: 8.82" Width: 6.23" Height: 0.52"
Weight:   0.8 lbs.
Binding  Hardcover
Publisher   World Scientific Publishing Company
ISBN  9810242077  
ISBN13  9789810242077  


Availability  0 units.


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