Approximation of Semicontinuous Functions

I came across this looking for a wrong theorem. Sorry if it is too late. I would avoid taking sups because they may not preserve smoothness. But if you know an increasing sequence of continuous functions that converge to your lsc function, you may obtain smooth ones by removing $2^{-n}$ to the current function, approximate it within $2^{-n-2}$ by a smooth function (but in the whole space $R^d$ a brutal convolution will not work, I don't know a better way than using partitions of unity before you convolve). Anyway, your new sequence is smooth and still increasing, and converges to the same limit. Agreed, this will not be nonnegative if your initial function $f$ was zero somewhere. For that case I am afraid I see no way to avoid doing this by hand, working on the open set where $f > 2^{-n}$, doing the same sort of thing as above there, and gluing by hand in the remaining region. (Sorry, did not spend too much time).