Dense jumps do not prevent Riemann integrability
= Dense jumps do not prevent Riemann integrability
A <left-continuous cumulative function of an atomic measure> with positive masses at a dense countable set has dense discontinuities. Nevertheless it is bounded and monotone on a compact interval, hence a <Riemann-integrable function>. Finite step-function sums approximate it uniformly because the positive masses are summable. Thus dense discontinuities do not imply failure of the <Riemann integral>.