# $\sigma$-algebra vs. $\sigma$-field: is there any difference?

The subject says it all: is there any difference between the two concepts of $\sigma$-algebra and $\sigma$-field? In probability theory, they seem to be used more or less interchangeably. If there is no difference, is there any historical reason why some people/schools use the term $\sigma$-algebra, while others use the term $\sigma-$field?

• Alternate names for the same thing. Each coming from a different part of mathematics. Mar 18 '17 at 21:43
• @GEdgar Which parts? Mar 18 '17 at 21:49
• In general, the term $\sigma$-algebra is used by people doing pure analysis, and the term $\sigma$-field is used by probability theorists. They are the same thing, however. Mar 18 '17 at 22:17
• According to all I have read about this, they are the same thing, it is just that, for the name $\sigma$-field, it is more widely used when we are talking something related to probability theory.
– BAI
Jul 25 '17 at 13:25