compressive sampling

just came across a new take on an old problem: compressed sensing. here's a gentle introduction to the subject. looks like youtube has some interesting lectures on this, too, especially linking compressive sensing or sampling to information theory. one thing that occurred to me is that the sparseness object expressed by the '0-norm' requires the part of the domain where the function goes to zero to do so faster than the norm parameter. otherwise, the 0^0 would be 1, just like x^0==1 for x!=0. so, something like lim x->0 exp(-1/x)^x. maybe i can think of it as an epsilon-norm, where epsilon is infinitessimal for all non-zero quantities but not exactly zero for the norm of zero.