Let $(X, T)$ be a topological dynamical system and $M(X)$ the set of all Borel probability measures on $X$ endowed with the weak$^*$ -topology. In this paper, it is shown that for a given sequence $S$ , a homeomorphism $T$ of $X$ has zero topological sequence entropy if and only if so does the induced homeomorphism $T$ of $M(X)$ . This extends the result of Glasner and Weiss [
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