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We show that for  any  ergodic Lebesgue measure preserving transformation   \begin{document}$ f: [0,1) \rightarrow  [0,1) $\end{document}   and  any  decreasing sequence   \begin{document}$ \{b_i\}_{i=1}^{\infty} $\end{document}   of positive real numbers with divergent sum, the set\begin{document}$   {\underset{n=1}{\overset{\infty}{\cap}} \, {\underset{i=n}{\overset{\infty}{\cup}}}\,} f^{-i}(B (R_{\alpha}^{i} x,b_i))  $\end{document}has full Lebesgue measure for almost every   \begin{document}$ x \in [0,1) $\end{document}   and almost every   \begin{document}$ \alpha \in [0,1) $\end{document}  . Here   \begin{document}$ B(x,r) $\end{document}   is the ball of radius   \begin{document}$ r $\end{document}   centered at   \begin{document}$ x \in [0,1) $\end{document}   and   \begin{document}$ R_{\alpha}: [0,1) \rightarrow  [0,1) $\end{document}   is rotation by   \begin{document}$ \alpha \in [0,1) $\end{document}  . As a corollary, we provide partial answer to a question asked by Chaika (Question   \begin{document}$ 3 $\end{document}  , [ 2 ]) in the context of interval exchange transformations.

A shrinking target theorem for ergodic transformations of the unit interval