Bounded interval/Continuous function/Equidistant lower integral/Lower integral/Exercise

From Wikiversity
Jump to navigation Jump to search

Let be a bounded interval and let denote a continuous function which is bounded from below. Suppose that the supremum over all staircase integrals for the equidistant lower staircase functions exists. Show that then the supremum for all staircase integrals for lower staircase functions (that is, the lower integral)

exists and coincides with the supremum first mentioned.