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We prove a rearrangement inequality for the uncentered Hardy-Littlewoodmaximal function $M_{\mu}$ associate to general measure $\mu$ on $\mathbb{R}$.This inequality is analogous to the Stein's result  $cf^{**}(t)\leq(Mf)^{*}(t)\leq C f^{**}(t)$, where $f^*$ is the symmetricdecreasing rearrangement function of $f$ and $f^{**}(t)=\int_0^tf^*(x)dx$.  Moreover, we compute the best constant of $M_{\mu}$ on  $L^{p,\infty}(\mathbb{R},d\mu)$.

Rearrangement inequalities of the one-dimensional maximal functions associated with general measures