INTEGRATION BETWEEN THE LEBESGUE INTEGRAL AND THE HENSTOCK—KURZWEIL INTEGRAL
Its Relation to Local Convex Vector Spaces
by Jaroslav Kurzweil (Mathematical Institute of the Academy of Sciences, Czech Republic)
About the AuthorJaroslav Kurzweil is a professor at the Mathematical Institute of the Academy of Sciences of the Czech Republic. He is also the author of the other five books and has published 105 original papers.He retired in 1996 and was the Chairman of the Union of Czech Mathematicians and Physicists since 1996 till 2002. He was elected as the Honorary Foreign Fellow of the Royal Society of Edinburgh in 1978 and Corresponding Member of the Academie Royale de Belgique, Classe des Sciences.
The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear.
The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required.
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