I am attaching photos from the chapter "Sobolev Spaces". 
What the author does is that first he approximates a $W^{1,1}$ function by smooth functions that converge in the $\|\|_{W^{1,1}}$ norm, and hence also converge pointwise ae. Then he takes a line parallel to $x_1$ axis (this is in the second photo), and chooses a point of accumulation.
My question: the line parallel to the $x_1$ axis is of $0$ measure in $R^n$, where $n\geq 2$. How do we know that such a point of accumulation even exists?