3
$\begingroup$

I came across the term trace $\sigma$-algebra in the context of conditional probability. Does anyone know where it comes from? i found a reference to trace of a matrix here: https://mathshistory.st-andrews.ac.uk/Miller/mathword/ but that was it.

$\endgroup$
6
  • 1
    $\begingroup$ I guess you mean this wiki.unifiedmathematics.com/index.php?title=Trace_sigma-algebra "Trace" in this sense is not related to "trace" of a matrix. "Trace" of a matrix is translation of the German word "Spur". I do not know the origin of "trace" for sigma-algebra. $\endgroup$ Commented Feb 24, 2022 at 16:14
  • $\begingroup$ @GeraldEdgar In this context German "Spur" is a cognate of English "Spoor", which means trace or track (of an animal one is hunting). "Remnant" is, I think, an acceptable translation, and not inappropriate for this connotation. $\endgroup$ Commented Feb 24, 2022 at 16:26
  • $\begingroup$ It's a bit of mystery then. Maybe someone who knows will spot this in the million other things on this site and drop a line. $\endgroup$
    – TonyK
    Commented Feb 25, 2022 at 1:06
  • $\begingroup$ The question Origin of the term 'Trace Topology' also found no trace (ouch) of the origin of a closely related term. $\endgroup$ Commented Feb 25, 2022 at 15:57
  • 1
    $\begingroup$ A similar use of "trace", in a colloquial sense as "residue" (in a colloquial sense) or "leftover", occurs in PDE and Sobolev space theory, where the question is about the shift in Sobolev (or other) indices in restricting a function to the boundary of a region, etc. $\endgroup$ Commented Apr 25 at 15:35

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.