A measurement apparatus will have a finite resolution set by the discretization of its possible outputs into bins, with the probability of lying within one of the bins given by the Born rule. We will consider the most common experimental situation, in which the bins are of uniform size. Let δx be a measure of the spatial resolution. We take the zeroth bin to be centered near the origin, with possibly some small constant offset c. The probability of lying within the jth interval of width δx is P ⁡ ⁡ [ x j ] = ∫ ∫ ( j − − 1 / 2 ) δ δ x − − c ( j + 1 / 2 ) δ δ x − − c | ψ ψ ( x ) | 2 d x