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!)



What does the σ in σ-algebra stand for?
From [Elstrodt's book](http://books.google.com/books?id=WECVEDeljqgC&printsec=frontcover&dq=elstrodt+integrationstheorie&hl=de#v=onepage&q&f=false) *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](http://books.google.com/books?id=WECVEDeljqgC&printsec=frontcover&dq=elstrodt+integrationstheorie&hl=de#v=onepage&q&f=false), 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](http://books.google.com/books?id=WECVEDeljqgC&printsec=frontcover&dq=elstrodt+integrationstheorie&hl=de#v=onepage&q&f=false), 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*. 


