This is about how random variables are defined. In some texts, I see that a random variable is associated with the sample space of random experiments, that is experiments with more than one possible outcome while in other texts, I see that a random variable is simply a real valued function of sample space (the experiment could be random or deterministic).
I'm confused– If the experiment is deterministic, that is, the experiment has only one possible outcome. Would it be correct to call it a random variable on such a sample space which is a singleton set?
Does the definition of random variable require you to consider sample space of random experiments (aka non-deterministic experiments) only?
This is the same sort of thing as counting a square as a special case of a rectangle. In mathematics we've learned over time that it's not worth excluding special cases from our definitions; "random" includes the special case of determinism, which is just when a specific outcome happens with probability $1$.
There are many reasons we've learned to do this; a simple one in this context is that we want to perform operations on random variables, such as adding them or applying functions to them, and it can happen that operations performed on "actually random" random variables can produce deterministic ones (for example taking certain limits). So we include all of them so we can talk about all of them uniformly.