The $()^c$ means the complement of whatever there's in the bracket in respect to $\Omega$
i just want to know what this big U and the flipped U means. Also what's the Latex-Symbol?
Best Answer
If $\mathcal{M}$ is a collection of sets, then $\bigcup_{M\in\mathcal{M}} M$ denotes the union of all the elements of $\mathcal{M}$. For instance, if $\mathcal{M}=\{A,B,C\}$, then $\bigcup_{M\in\mathcal{M}} M=A\cup B\cup C$. More precisely, $$\bigcup_{M\in\mathcal{M}} M=\{x:\text{there exists } M\in\mathcal{M}\text{ such that }x\in M\}.$$
Similarly, $\bigcap_{M\in\mathcal{M}} M$ denotes the intersection of all the elements of $\mathcal{M}$. The LaTeX command for $\bigcup$ is \bigcup and the command for $\bigcap$ is \bigcap.
More generally, $$\bigcup_{M\in\mathcal{M}}[\text{some expression involving $M$}]$$ denotes the union of the expressions for all elements $M$ of $\mathcal{M}$. So in your example, $\bigcup_{M\in\mathcal{M}} M^c$ denotes the union of all the complements of elements of $\mathcal{M}$. You should think of this similar to summation notation, except you are taking a union instead of a sum.
The symbol denotes whatever the author tells you it will denote in his comments about notation, and there is a special place in hell for users of unexplained notation.
Best Answer
If $\mathcal{M}$ is a collection of sets, then $\bigcup_{M\in\mathcal{M}} M$ denotes the union of all the elements of $\mathcal{M}$. For instance, if $\mathcal{M}=\{A,B,C\}$, then $\bigcup_{M\in\mathcal{M}} M=A\cup B\cup C$. More precisely, $$\bigcup_{M\in\mathcal{M}} M=\{x:\text{there exists } M\in\mathcal{M}\text{ such that }x\in M\}.$$
Similarly, $\bigcap_{M\in\mathcal{M}} M$ denotes the intersection of all the elements of $\mathcal{M}$. The LaTeX command for $\bigcup$ is \bigcup and the command for $\bigcap$ is \bigcap.
More generally, $$\bigcup_{M\in\mathcal{M}}[\text{some expression involving $M$}]$$ denotes the union of the expressions for all elements $M$ of $\mathcal{M}$. So in your example, $\bigcup_{M\in\mathcal{M}} M^c$ denotes the union of all the complements of elements of $\mathcal{M}$. You should think of this similar to summation notation, except you are taking a union instead of a sum.