TITLE: What does the σ in σ-algebra stand for?
QUESTION [18 upvotes]: I was tutoring someone in analysis and realized I have no idea where this notation comes from (or analogous terms: σ-additive, σ-ring, etc). I would like to know why the letter σ was chosen. I can't think of anything relevant that starts with "S" in either English or French. My German is nearly nonexistent, but I didn't see an explanation while trying to read the German wikipedia page.
Bonus points if you can tell me who introduced this notation and when.
(By the way, I really don't like this notation very much. I think it would be much more reasonable if we just wrote "$\aleph_1$-algebra" instead. Or better yet, replaced "algebra" with a less overloaded word. But I might change my mind, if it turns out there is a good explanation for the σ!)

REPLY [42 votes]: From Elstrodt's book Maß- und Integrationstheorie,  pages 13-14:

Bei den Wörtern „$\sigma$-Ring", „$\sigma$-Algebra" weist der Vorsatz „$\sigma$-..." darauf hin, daß das betr. 
  Mengensystem abgeschlossen ist bez. der Bildung abzählbarer Vereinigungen. Dabei soll der 
  Buchstabe $\sigma$ an „Summe" erinnern; früher bezeichnete man die Vereinigung zweier Mengen als ihre Summe (s. z.B. F. Hausdorff 1, S. 5 und S. 23).
  Eine entsprechende Terminologie ist  üblich mit dem Vorsatz „$\delta$..." für abzählbare Durchschnitte (z.B.„$\delta$ -Ring"). 

My translation:                 

In the words "$\sigma $-ring","$\sigma$-algebra" the prefix "$\sigma$-..." indicates that the system of sets considered is closed with respect to the formation of denumerable unions. Here the letter $\sigma$ is to  remind one of "Summe"[sum]; earlier one refered to the union of two sets as their sum (see for example F. Hausdorff 1, p. 5 and p. 23).
  A corresponding terminology is usual with the prefix „$\delta$-..." for denumerable intersections [Durchschnitte] (for example "$\delta$ -ring")  

(The reference is to Hausdorff's Grundzüge der Mengenlehre. published in 1914.) 
To sum up: the excerpt says that $\sigma$ [=Greek s] and $\delta$[=Greek d] come from the German words Summe and Durchschnitt, whose English  translations are  respectively sum and  intersection.