Henstock-Kurzweil integral
The Henstock-Kurzweil integral (also known as the Generalized Reimann integral) is one of the most widely applicable generalizations of the Reimann integral, but it also uses a strikingly simple and elegant idea. It was developed independantly by Ralph Henstock and Jaroslav Kurzweil
Definition
Let
Let
We say that is Generalised Reimann Integrable on
if and only if,
, there exists a gauge
such that,
if is a
-fine tagged partition on
, then
Here, is the Reimann sum of
on
with respect to
The elegance of this integral lies in in the ability of a gauge to 'measure' a partition more accurately than its norm.
See Also
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