[jlokier]

Those notations are well-known standard notation for the same general concept, "the size of".

What "the size of" means is different applied to each type of object, and may have to be defined to explain some of them (esp. |f|), but it's common in math that general concepts apply differently to different things, while having some properties in common.

I think the notation is helpful rather than confusing because "the size of" carries with it some intuitive connotations which are common to each of those examples.