The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic ‘truth’ for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the ‘truth-values’ for such assertions are elements of iterated boolean measure-algebras (mathbb{A}) (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).