As many people on this site know, and could probably recite by heart at any minute, the definition of a $\sigma$-finite measure is as follows:
Let $(X, \mathcal{F}, \mu)$ be a measure space. The measure $\mu$ is said to be $\sigma$-finite if there exist $\{E_n\}_{n=1}^{n=\infty} \subseteq \mathcal{F}$ satisfying:
(i) $\cup_{n=1}^{\infty} E_n = X$
(ii) $\mu(E_n)$ is finite for all $n$
There is also the definition of a $\sigma$-algebra, namely a collection of subsets of $X$ that (i) contains $X$ (ii) is closed under complements and (iii) is closed under countable unions.
Question: Why is the Greek lowercase letter $\sigma$ used as an adjectival modifier in the above definitions? Does the letter $\sigma$ have some connection with the word "countable"?
(Obviously, I am well aware that the capital $\Sigma$ is very much associated with summations, and these summations are often considered over a countable indexing set (although not always!), so perhaps there is some connection here. But on the other hand, if there is such a strong association with uppercase $\Sigma$ and "countableness", then why don't we call it a $\Sigma$-measure or a $\Sigma$-algebra?)