I have a function $f$ defined on $(-a,a)$ as $f(x) = 1$ when $x = 0$ and $0$ elsewhere. There is a sequence of smooth functions $\{f_n\}$ defined on $(-a,a)$, such that $f_n\to f$ pointwise. Also $V(f_n)\to V(f) = 2$ where $V(f)$ is the variation of function $f$ in the inetrval $(-a,a)$. Lets de...