Notation of a random variable, $\xi$ versus $X$ I'm reading Kallenberg's foundations of modern probability 2nd Ed (Early chapters). He uses $\xi$ as the notation for a random variable whereas almost all other books (e.g. Durrett's probability:Theory and Examples) use $X$ as the notation for a random variable. I think when it comes to stochastic processes, he then switches to $X_t$.
I'm just curious what the reasoning behind his use of Greek alphabets is? Is this the consensus for some publications? Is this like a historic thing?
 A: There is no particular reason to use either $X$ or $\xi$ and there is no real consensus which symbol one should use. It is rather a matter of convenience:

It is convenient to denote a random variable similarly to, but differently from, its values.

Since the most commonly used symbols for unknown (real) values are $x,y,z$, and since it is convenient to be able to write expressions like

A random variable takes a given value

by a coincise formula like
$$X=x,$$
the habit took hold to denote random variables by $X,Y,Z$. It is particularly used in textbooks, where it is necessary to distinguish a variable from its values as this distinction may not be apparent from context to the reader. In research papers it is not unusual to use $x$ for random variables and write instead something like
$$x=x_0.$$
This holds mostly for real-valued random variable, but it does not make much sense for random variables with special values:

the notation for random variables is usually superseded by the standard notation for the objects they describe.

That is, it is unusual to denote a random angle by $X$, and one would use instead $\theta$ or even $\omega$.
Greek letters are be introduced because

the notation for random variables is usually superseded by the standard notation for other objects, if the two are conflicting

It is quite common to use $X$ for topological spaces or measurable/measure space, so in this case you would not use $X$ to denote a random variable with values in some such space, and prefer $X$ to indicate the space. The random variable could then be named $\xi$, and one could  write $\xi=x$ to indicate that the r.v. $\xi$ takes the value $x\in X$.
Finally, there is a tendency to avoid capitalization, as formulas become cumbersome to read. The reasonable alternative is to use Greek letters, since they can still be reasonably paired with Latin ones.
