Theorem 1(PDF Projection theorem), see [3,5].
Let
be a mapping from
to
, .
Let
be an arbitrary feature PDF with support .
Let
be a reference distribution with support .
Let
, the distribution imposed on
when
and
.
Let
be non-zero and have finite value everywhere on .
Then, the function (2.2)
is a PDF (integrates to 1 over ), and is a member of
.

Proof: These assertions are proved in Section 16.4.
See also [3] or [5], Theorem 2.