I have problem with some mathematics language. Can some one interpret for me?

1) a function $\displaystyle f_x : R \rightarrow [0,\infty] $. Is this means ' function fx consists of variable which is real numbers and the outcome of function fx is from 0 to infinity'?

2) a function $\displaystyle f_x : (-c,c) \mapsto R $

2) $\displaystyle P(X \in R \setminus \{x_1,x_2\})$

3) Random variable $\displaystyle T_1 = inf\{i \leq 0: \epsilon_{i+1}=1\} $

4) A probability measure on a sample space $\displaystyle \Omega$ is a function A $\displaystyle \mapsto$ P(A) of event $\displaystyle A \subseteq \Omega$