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.

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    $\begingroup$ 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
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    $\begingroup$ 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


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