Before revision:  Specifically, given n observations from the discrete distribution, if some estimator incurs an error \varepsilon with probability at most \delta, then plugging in the PML distribution incurs an error 2\varepsilon with probability at most \delta  \exp(3n).
After revision:  Specifically, given n observations from the discrete distribution, if some estimator incurs an error \varepsilon with probability at most \delta, then plugging in the PML distribution incurs an error 2\varepsilon with probability at most \delta \cdot \exp(3n).