Oscillation of a function on an interval
= Oscillation of a function on an interval
{title2=$\operatorname{osc}_I f=\sup_I f-\inf_I f$}
For a bounded real function, its oscillation on an interval is its full range width there. An <upper Darboux sum> minus a <lower Darboux sum> is the sum of these widths multiplied by their interval lengths. This gives the <Riemann integrability criterion> in terms of oscillation.