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In this paper, we introduced the mildly version of the Hurewicz basiscovering property, studied by Babinkostova, Ko\v{c}inac, and Scheepers. A space$X$ is said to have mildly-Hurewicz property if for each sequence $\langle\mathcal{U}_n : n\in \omega \rangle$ of clopen covers of $X$ there is asequence $\langle \mathcal{V}_n : n\in \omega \rangle$ such that for each $n$,$\mathcal{V}_n$ is a finite subset of $\mathcal{U}_n$ and for each $x\in X$,$x$ belongs to $\bigcup\mathcal{V}_n$ for all but finitely many $n$. Then wecharacterized mildly-Hurewicz property by mildly-Hurewicz Basis property andmildly-Hurewicz measure zero property for metrizable spaces.

Mildly version of Hurewicz Basis covering property and Hurewicz measure zero spaces