### Statement of the PDF Projection Theorem

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.

Baggenstoss 2017-05-19