Difference between "and" and "such that" I have some problems identifying the essential difference between using "and" and "such that" in statements. Consider the property of holding almost everywhere i.e
$$ \exists N \in \mathcal{F} \,\,\text{s.t} \,\,\mu(N) = 0  \,\,\text{s.t} \,\,\ \forall x \in \Omega \setminus N , P(x) \ \text{holds}$$
$$ \exists N \in \mathcal{F}  \,\,\text{s.t} \,\,(\mu(N) = 0 \wedge \forall x \in \Omega \setminus N , P(x) \ \text{holds})$$
somone know how to think about this?
 A: "Such that" is technically not a part of a structured logical sentence - it is simply a phrase we insert to make the sentence more English-like. This is used after an existential quantifier $\exists$. E.g. the sentence $\exists n (n+n=n)$ could be rendered in natural language as "there exists $n$ such that $n+n=n$" (note how we inserted this phrase which was not present in the logical sentence).
In contrast, and ($\land$) is a logical symbol and a necessary part of the sentence. Your second example is correct, not the first.
A: When in the scope of an existential quantifier $\exists$, "such that" usually stands for "and", from a logical point of view, when it connects more elementary statements. 
In particular, your two statements are logically equivalent, even though the second one is slightly more elegant from a grammatical point of view. 
Their rigorous logical form is the following:
\begin{align}
\exists N \, (N \in \mathcal{F} \land \mu(N) =0 \land \forall x (x \in \Omega \setminus N \to P(x)))
\end{align}
