  We introduce Strong Measuring, a maximal strengthening of J. T. Moore's
Measuring principle, which asserts that every collection of fewer than
continuum many closed bounded subsets of $\omega_1$ is measured by some club
subset of $\omega_1$. The consistency of Strong Measuring with the negation of
CH is shown, solving an open problem from about parametrized measuring
principles. Specifically, we prove that Strong Measuring follows from MRP
together with Martin's Axiom for $\sigma$-centered forcings, as well as from
BPFA. We also consider strong versions of Measuring in the absence of the Axiom
of Choice.
