Why are open sets denoted $U$, $G$, and measurable sets $E$?

Question

Why are open sets usually denoted by $U$? Is there a reference about this? Sometimes open set uses the letter $G$, such as $G_{\delta} $ set. I also wonder the meaning of $G$.

Additional question: Why do we use or who first used $E$ to denote a subset in measure theory?

Answer 1

$U$ stands for Umgebung. Reference: https://de.m.wikipedia.org/wiki/Umgebung_(Mathematik) This is the German wikipedia article corresponding to Neighborhood. More complete history on this in Why do we traditionally use letter U for open sets?

$E$ stands for Ensemble, which is French for set. You can see it used in Lebesgue’s original paper to denote arbitrary measurable sets, so that it became tradition https://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral

Answer 2

For $G_\delta$ set and $F_\sigma$ set, each of this is from german word Gebiet and french word fermé respectively.