It's L^2 in finite dimensional spaces also - you can just as well define || v || = \int |v_i| dC(i) (where C is the counting measure). Finite dimensional spaces can also be interpreted as functions, i.e. C^3 is the same as {1,2,3} => C.
This is a rationalization but it's useful. We have a physical theory in L^2, and we know that you can't have such a theory in L^2.1 or L^7. Our theories might be totally wrong. But we are confident they can't be only a little wrong.
This is a rationalization but it's useful. We have a physical theory in L^2, and we know that you can't have such a theory in L^2.1 or L^7. Our theories might be totally wrong. But we are confident they can't be only a little wrong.