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The proofs of Theorem 3.1 and Corollary 4.1 in Le~ao and Ohashi (2013) are incomplete. The reason is a wrong statement in Remark 2.2. The hypotheses and statements of Theorem 3.1 and Corollary 4.1 in Le~ao and Ohashi (2013) remain unchanged but the proofs have to be modified. In this short note, we provide the details.

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