I'm not sure commission/omission distinction is really the key here. This becomes clearer by inverting the situation a bit:

Some third party is about to forcibly wirehead all of humanity. How should your moral agent reason about whether to intervene and prevent this?

I'm not sure what you're trying to construct, but note that one can only multiply distributions under rather restrictive conditions. There are some even more abstract classes of distributions which permit an associative multiplication (Colombeau algebras, generalized Gevrey classes of ultradistributions, and so on) but they're neither terribly common nor fun to work with.

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) dxI 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. :)