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In this very short note we rectify this issue exhibiting a simple example of a Markov-Feller semigroup enjoying the asymptotic strong Feller property, for which the e-property is not satisfied. (See also the comment on a connection between the asymptotic strong Feller property and the e-property by T. Szarek, D. Worm [ETDS 32 (2012), {\\S} 1]). 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