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How to Integrate Any Real Function

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Book cover Hypernumbers and Extrafunctions

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

In this chapter, we study problems of integration, demonstrating the advantages that transition to hypernumbers and extrafunctions gives for this field. It is well known that it is possible to integrate only some real functions. Shenitzer and Steprāns (1994) explain that while in the eyes of some mathematicians the Lebesgue integral was the final answer to the difficulties associated with integration and there is no perfect integral, there were others who were not willing to give up the search for the perfect integral, one which would make all functions integrable. Although efforts of different mathematicians extended the scope of integrable functions, their results only gave additional evidence for impossibility of such a perfect integral.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, 90095, USA

    Mark Burgin

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  1. Mark Burgin
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© 2012 Mark Burgin

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Burgin, M. (2012). How to Integrate Any Real Function. In: Hypernumbers and Extrafunctions. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9875-0_5

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