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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?

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    $\begingroup$ Alternate names for the same thing. Each coming from a different part of mathematics. $\endgroup$
    – GEdgar
    Mar 18 '17 at 21:43
  • $\begingroup$ @GEdgar Which parts? $\endgroup$
    – Anonymous
    Mar 18 '17 at 21:49
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    $\begingroup$ 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. $\endgroup$ Mar 18 '17 at 22:17
  • $\begingroup$ 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. $\endgroup$
    – BAI
    Jul 25 '17 at 13:25
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If you want to be completely sure you can see Taylor´s Introduction to Measure and Integration where he state that both concepts refer to the same thing.

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