Suppose that $([0,1],B([0,1]),\mu)$ is a measure space, here $B([0,1])$ is the set of all Borel sets on [0,1], let $N_{\mu}$ be the set of all subset S of $[0,1]$ such that S is $\mu$-negligible, let $M$ be the set of all meager sets contained in $[0,1]$, I want to show that there is no finite Borel measure $\mu$ on $[0,1]$ such that $N_{\mu}=M$, how to show this? can anyone help me? thank you in advance

Suppose that $([0,1],B([0,1]),\mu)$ is a measure space, here $B([0,1])$ is the set of all Borel sets on $[0,1]$, let $N_{\mu}$ be the set of all subsets $S$ of $[0,1]$ such that $S$ is $\mu$-negligible, let $M$ be the set of all meager sets contained in $[0,1]$. I want to show that there is no finite Borel measure $\mu$ on $[0,1]$ such that $N_{\mu}=M$, how to show this? Can anyone help me? Thank you in advance!