[再寄小读者之数学篇](2014-09-22 distributions and square integrable functions)

Suppose that $fin L^2$, $gin scrD'$, if $$ex f=g,mbox{ in }scrD', eex$$ then $f=gin L^2$.

In fact, $scrDsubset L^2 a L^2subsetscrD'$. Thus $h=f-g=0in scrD'$, the zero element is the same in $L^2$ and $scrD'$, and hence $h=f-g=0in L^2$, $g=f-(f-g)in L^2$.