# Help on concentration of measure problem

I am trying to solve the following exercise (exercise 8.1 from Bucheron, Lugosi, Massart):

Use Marton's transportation inequality to show that if $$P$$ is a product measure on $$\mathcal{X}^n$$, then for any pair of measurable sets, $$A, B \subset \mathcal{X}^n$$, $$d_H(A, B) \leq \sqrt{\frac{n}{2} \log(1/P(A))} + \sqrt{\frac{n}{2} \log(1/P(A))},$$ where $$d_H(A, B) = \min_{x \in A, y \in B} \sum_{i=1}^n \mathbf{1}_{\{x_i \neq y_i\}}$$.

I could really use a hint!