Let $(X,\tau)$ be a topological space. Denote by $Bor(X)$ the space of Borel functions $f:X\to\mathbb{R}$ where we identify two functions whenever they agree on the complement of a meager set. We endowed $Bor(X)$ with the pointwise partial order. I have read somewhere that this space is Dedekind complete. Is that true? Where can I find the proof worked out?