Proposition 21.11.43`281F97D00D5D`

Proposition 21.11.43.281F97D00D5D For any $F\in \mathcal{E}^{\infty }(N,P)$, we have $F^*|_{M\setminus P}\equiv \infty $ and $F^*$ is bounded on $P$.

Proof. From $F\sim \operatorname{Supp}_ P$, we take the Legendre transform to get $F^*\sim \operatorname{Supp}_ P^*=\chi _ P$, where we applied example 21.11.25. $\square$

Cite this page

BibTeX citation

@misc{pome-tag-281F97D00D5D,
  author = {{Pome contributors}},
  title = {Proposition 21.11.43},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/281F97D00D5D/}
}

Comments

Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.

Read this page’s discussion on GitHub Post a comment on GitHub

Proposition 21.11.43281F97D00D5D

Comments

Proposition 21.11.43`281F97D00D5D`