The structure of superposition is given by solution of the Schrodinger equation. It's often continuous, e.g. electron's s orbital in atom is a continuum of coor

The structure of superposition is given by solution of the Schrodinger equation. It's often continuous, e.g. electron's s orbital in atom is a continuum of coordinate eigenstates. In this case a discrete sum is replaced with an integral and Born rule becomes a function on this continuum, but a discrete case can be easier to understand, so I recommend to start with that. The proof follows the law of large numbers https://en.wikipedia.org/wiki/Law_of_large_numbers https://en.wikipedia.org/wiki/Law_of_large_numbers