 What follows is a brief sketch of von Neumann’s strategy. First, he recognized the mathematical framework of matrix mechanics as what would now be characterized as an infinite dimensional, separable Hilbert space. Here the term “Hilbert space” denotes a complete vector space with an inner product; von Neumann imposed the additional requirement of separability (having a countable basis) in his definition of a Hilbert space. He then attempted to specify a set of functions that would instantiate an (infinite-dimensional) separable Hilbert space and could be identified with Schrödinger’s wave mechanics. He began with the space of square-integrable functions on the real line. To satisfy the completeness condition, that all Cauchy sequences of functions converge (in the mean) to some function in that space, he specified that integration must be defined in the manner of Lebesgue. To define an inner product operation, he specified that the set of Lebesgue square-integrable functions must be partitioned into equivalence classes modulo the relation of differing on a set of measure zero. That the elements of the space are equivalence classes of functions rather than functions is sometimes overlooked, and it has interesting ramifications for interpretive investigations. It has been argued in Kronz (1999), for example, that separable Hilbert space is not a suitable framework for quantum mechanics under Bohm’s ontological interpretation (also known as  Bohmian mechanics).