This is a question about symbols and notation, so it is hard to post on
a text forum, but it has been driving me crazy so here goes. In the
book "Measure, Integral, and Probability" by Capinski and Kopp the
authors define the set inclusion notation "A subset B" (expressed here
in LaTeX) to mean x in A => x in B. The authors clarify that they do
not restrict themselves to a proper subset by this notation, ie A subset
B does not exclude the possibility that A = B. This is the usual subset
symbol without the line underneath.
Then throughout the book they interdisperse this notation with the
notation A subseteq B (the subset symbol with a line underneath) in
various definitions and theorems. The bizarre thing is that given their
convention for A subset B, it seems to me that the two notations should
mean *exactly* the same thing. This creates confusion (at least for me)
because if A subseteq B denotes the same thing as A subset B, then why
are they using both notations instead of one? If, on the other hand,
the two notations mean different things, and if A subset B includes the
possibility that A=B, then what can A subseteq B possibly mean?
I checked the errata sheet in the springer verlag website and there is
nothing there about this. Has anyone worked through the proofs in this
book and figured this out?
Thanks
-sto
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