Terminology of "Random variable" A random variable $X$ is a measurable function $X : \Omega \rightarrow E $ where $\Omega$ and $E$ are measurable sets. So, as far as I can see from this definition, random variables are just measurable functions. I can not see any randomness it it and I suppose it's also not a variable. Then what is the reason behind this terminology ? 
 A: You can think of a sample space $\Omega$ as the set of all possible outcomes from some experiment. A sigma algebra $\mathcal{F}$ on $\Omega$ consists of events, which are collections of outcomes. A probability measure $P$ defined on $\mathcal{F}$ tells you how likely events are. One can think of a sigma algebra as containing information that is available, because we can say something about an event in $\mathcal{F}$ (e.g., its probability), but not about subsets of $\Omega$ that are not in $\mathcal{F}$.
A random variable $X:\Omega \to E$ can be thought of as a measurement taken when some experiment has occurred. That is, $X$ takes outcomes (elements $\omega \in \Omega$) and tells us something about them (namely, $X(\omega)$). 
As an example, say $\Omega$ is the set of strings of $H$, $T$ of length $5$ (i.e., $\{HHHHH,HHHHT,HHHTH,\dots,TTTTT\}$, the outcomes of five coin flips), $\mathcal{F}$ is the power set of $\Omega$, and $X$ is the number of heads in an outcome. So, for example, $X(HHHHH)=5$, and $X(HTTHT)=2$. The "experiment" consists of flipping five coins (resulting in an outcome in $\Omega$), and the "measurement" $X$ tells us how many heads there were. In a sense you're right that $X$ isn't "random" - it deterministically maps outcomes in $\Omega$ to an integer in $\{0,1,2,3,4,5\}$. But randomness is encoded in the "experiment" itself, so in that sense $X$ is still a random quantity, and it makes sense to ask what, say, $P(X=3)$ is.
Because random variables are simply defined as measurable functions on probability spaces, they need not actually be "random" in the colloquial sense of the word. Constants are random variables (they are always measurable).
