I'd like to show that a measure preserving transformation $T:X\rightarrow X$ is recurrent iff it has no wandering sets of positive measure.
I'm working from the following definitions: a measurable set $W$ is wandering if for all $i,j\ge 0 ; i \neq j$ we have $T^{-i}(W) \cap T^{-j}(W) = \emptyset$, and a measure preserving transformation is recurrent if for every measurable set $A$ with nonzero measure, for almost all $x \in A$ there is some $n \in \mathbb{N}$ such that $T^n(x) \in A$.
I assume you work with finite measure spaces.
Assume $T\colon X\to X$ recurrent. Let $W$ be a wandering element. Assume that $W$ has non-zero measure. Then $\mu\left(W\cap\bigcup_{n\geqslant 1}T^{-n}W\right)=\mu(W)$, but the LHS is $0$ since $W$ is wandering.
Assume that $T\colon X\to X$ is not recurrent. Then there is $A$ of positive measure such that $\mu\left(A\cap\bigcup_{n\geqslant 1}T^{-n}A\right)<\mu(A)$. Define $$W:=A\cap\bigcap_{n\geqslant 1}T^{-n}\left(X\setminus A\right).$$ Then $W$ is a wandering set of positive measure.