The talk aims at a dynamical Borel-Cantelli lemma for Poincarérecurrence theorem. More precisely, in a measure preserving dynamical system $(X, T, \mu)$ with some regular conditions, the $\mu$-measure of the following set

\[\Big\{x\in X: |T^nx-x|<\psi(n), \ {\text{for infinitely many}}\ n\in \mathbb{N}\Big\}\]

obeys a dichotomy law according to the divergence or convergence of certain series. Our setting also unifies the cases of the recurrence property and the shrinking target problem in dynamical systems.