The Darboux Integrability Condition - Real Analysis | Lecture 19

In this lecture we introduce an equivalent condition to determine if a function is Riemann integrable. The condition is due to French mathematician Gaston Darboux and characterizes integrability without using evaluation points. Instead, Darboux's condition defines upper and lower integrals using maximal and minimal values of the function over each subinterval. In the case of Riemann integrability, we see that the upper and lower sums converge to each other, resulting in the value of the Riemann integral.

This course is taught by Jason Bramburger.