Riemann-Stieltjes integral
= Riemann-Stieltjes integral
{c}
{title2=$\int_a^b f\,dg$}
For continuous $f$ and an integrator $g$ of <bounded variation>, the Riemann-Stieltjes integral is the limit of tagged sums $\sum f(\xi_j)(g(t_{j+1})-g(t_j))$ as the mesh tends to zero. It exists and equals integration against the signed measure induced by $g$. Continuous vector-valued integrators are handled componentwise, which defines <path signatures> of continuous <bounded variation> paths.