Frenchel-Moreau Theorem(FASSPDE)

In order for convenience in checking definition along learning in Math, I found it necessary to gather definitions of the same kind so that distinguishing the differences among them will no longer be a tedious job. This work is very hard to do even many materials are available, if you want to use for commercial use, please contact me for permission. Furthermore, the work is still long from finished, if you want to contribute for more or better definitions, please contact me.

Tianyu Zhang

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Theorem 1.7 Frenchel-Moreau Theorem


A convex, l.s.c. function which is not identically infinity, coincides with its dual.

Proof(See Appendix Above)


Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

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