Normal-state quantum measurement interpretation

Adopt the following measurement interpretation for this nonrelativistic quantum-statistical model. A prepared normal state is a trace-class density operator $\rho$ on a specified separable complex Hilbert space $H$. A sharp measurement of a self-adjoint observable $A$, with spectral PVM $E_A$, assigns probability ${\mathbb{P}}_{\rho }\{A\in C\}=\mathrm{Tr}(\rho E_A(C))$ to each Borel outcome set $C\subseteq \mathbb{R}$. Finite projective measurements use the same rule with their orthogonal projections. This adopts a physical probability interpretation for the mathematical state law proved in Trace-state cyclicity and spectral probability calculus; it does not derive the Born rule, assert that an apparatus realizes a specified PVM, or report experimental outcomes. Infinite algebraic states not represented by trace-class density operators are not included.

The Axiom of Choice is inherited from the unbounded spectral theorem and its spectral-calculus supplier closure. Its strength is retained in the mathematical dependencies. The scalar probability and bounded cyclicity clauses now use the exact canonical suppliers cited by Trace-state cyclicity and spectral probability calculus; this source adoption supplies no native readiness or empirical validation, and implies no weaker foundation.