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The Fourier transform is a bijection in
As mentioned at
Section "Plancherel theorem"
, some people call this part of
, while others say it is just a corollary.
This is an important fact in
, since it is because of this that it makes sense to talk about
position and momentum space
as two dual representations of the
that contain the exact same amount of information.
Lebesgue integral of
is complete but Riemann isn't
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