  We prove that on a compact K\"ahler manifold, the non-pluripolar
Monge-Amp\`ere mass of a $\theta$-psh function decreases as the singularities
increase. This was conjectured by Boucksom-Eyssidieux-Guedj-Zeriahi who proved
it under the additional assumption of the functions having small unbounded
locus. As a corollary we get a comparison principle for $\theta$-psh functions,
analogous to the comparison principle for psh functions due to Bedford-Taylor.
