Left-continuous cumulative function of an atomic measure
= Left-continuous cumulative function of an atomic measure
{title2=$F(x)=\mu(( -\infty,x))$}
For positive summable weights $w_j$ at points $q_j$, the strict cumulative function $F(x)=\sum_{q_j<x}w_j$ is nondecreasing and left-continuous. A finite-head/tail argument proves left-continuity, and its right jump at an atom is the mass there. This strict convention differs at atoms from the usual right-continuous <cumulative distribution function>.