  Using an infinitary version of the Hypergraph Removal Lemma due to Towsner,
we prove a model-theoretic higher amalgamation result. In particular, we obtain
an independent amalgamation property which holds in structures which are
measurable in the sense of Macpherson and Steinhorn, but which is not generally
true in structures which are supersimple of finite SU-rank. We use this to show
that some of Hrushovski's non-locally-modular, supersimple $\omega$-categorical
structures are not MS-measurable.
