J. Alan Alewine - Vanderbilt University
Riemann Revisited: An Introduction to the Kurzweil-Henstock
Integral
In the early twentieth century, Denjoy and Perron independently created an integral that generalized that of Lebesgue's. It has the property that it can integrate the derivative of any function, a feature the Lebesgue integral lacks. However, their integral has one primary drawback---its definition is complicated. In the 1950's, Kurzweil and Henstock independently discovered an integral that is equivalent to that of Denjoy's and Perron's but whose definition is much less complicated. Their definition is strikingly similar to the definition of Riemann's integral. This modification led to a powerful integral with a fairly simple definition.
This talk will primarily serve as an introduction to the Kurzweil-Henstock, or KH, integral, but will end with a discussion about a new topology we have placed on the space of all KH-integrable functions.
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