How to read equation for summing probabilities of each member in a set?

Question

I’m reading through a chapter in https://www.probabilitycourse.com

There is a section ...

Consider a discrete random variable X with range $Range(X)=R_X$. Note that by definition the PMF is a probability measure, so it satisfies all properties of a probability measure. In particular, we have

• $0 \leq P_X(x) \leq 1$ for all $x$, and
• $\Sigma_{ x \in R_X}P_X(x)=1$

How do I read the bottom equation? Is it ...

Sum of all the probabilities of X for each x in $R_X$

Answer 1

You sum over all x's which are in $R_x=Range(X)={x \in \mathbb{R} | x=X(\omega) }$ for some $\omega$ in the sample sample}.

So yes, you read that correctly.