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Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear -algebras in the UCT class is quasidiagonal. Building on their work, we generalise the result, and show that any faithful, amenable trace on a separable, exact -algebras in the UCT class is quasidiagonal. We also prove that any amenable trace on a separable, exact, quasidiagonal -algebra in the UCT class is quasidiagonal.

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