18/01/23 22:05:02.39 mULB7oqE.net
>>83 つづき
As can be seen from the definition, the gauge integral has very much the same flavor as the Riemann integral, being obtained from a slight modification of the Riemann integral, and does not require a lot of technical apparatus for its introduction as is the case for the Lebesgue integral.
However, despite the elementary appearance of the gauge integral, it leads to a very powerful theory of integration which encompasses the Riemann integral, the Cauchy-Riemann (improper Riemann) integral, and the Lebesgue integral.
For this reason, the gauge integral would seem to be a very reasonable candidate for inclusion in an introductory real analysis course; it is as conceptuall