Outer measure and set with full measure I've seen two different definitions for an outer measure $\mu$ on $\mathcal{P}(X)$, where $X$ is a set, obtained from a given probability measure on $X$.
D1 = a set of full outer measure is a subset $A\subseteq X$ such that $\mu(A)=1$. 
D2 = a set of full outer measure is a subset $A$ such that $\mu(X\backslash A)=0$. 
Since outer measures are not additive, I'm having trouble seeing how those two definitions are equivalent. Clearly D2 implies that a set with full outer measure is measurable (for the sigma algebra generated by $\mu$), however it's not clear to me that it's the case for D1.   
So my question is : are those definitions equivalent ? 
My follow up question is : when we say that $C([0,1])$ has full outer measure for the Wiener measure on $\mathbb{R}^{[0,1]}$, are we using Definition D2, or D1 ?

D1 and D2 are not equivalent in general. 
Consider $X=[0,1]$ and $\mu=$ Lebesgue outer measure
By this thread, there is a non-measurable set $V$ with $\mu(V)=1$, so $V$ is a set of full measure in the sense of D1. However, as you pointed out, any set of full measure in the sense of D2 must be measurable, so $V$ is not such a set.
I do not have knowledge on Wiener measure so I leave it to someone who know it well. 
