Ah, nevermind then. I was thinking something like let b(x,k) = 1/sqrt(2k) when |x| < k and 0 otherwise
then define integral B(x)f(x) dx as the limit as k->0+ of integral b(x,k)f(x) dx
I was thinking that then integral (B(x))^2 f(x) dx would be like integral delta(x)f(x) dx.
Now that I think about it more carefully, especially in light of your comment, perhaps that was naive and that wouldn’t actually work. (Yeah, I can see now my reasoning wasn’t actually valid there. Whoops.)
Ah well. thank you for correcting me then. :)