= Stieltjes bilinear functional under a variation constraint
{c}
{title2=$T(F,G)=\int_0^uG\,dF$}
On bounded continuously differentiable functions with uniformly bounded <total variation of a function>, the map $T$ is <Hadamard differentiable> in the <supremum norm> with <derivative> $\dot T_{F,G}(a,b)=\int_0^ubF^{\prime}+G(u)a(u)-G(0)a(0)-\int_0^uG^{\prime}a$. Use <weak convergence of bounded-variation integrators> for the first term and <integration by parts> for the remaining terms. No <derivatives> of the limiting continuous directions are required.
Back to article page
