jerrylicious/garden
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Added bornological spaces.

Browse Source
This commit is contained in:
Bokuan Li
2026-05-02 15:59:03 -04:00
parent dcf11fb978
commit 1e53581113
8 changed files with 82 additions and 22 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
src/measure/vector/vector.tex
View File

@@ -34,7 +34,7 @@
\sup_{A \in \cm}|\dpn{\phi, x_A}{E^{**}}| = \sup_{A \in \cm}|\dpn{\mu(A),\phi}{E}| < \infty
\]
By \autoref{proposition:bornologic-continuous-complete} and \autoref{proposition:metrisable-bornologic}, $E^*$ is a Banach space. The \hyperref[Uniform Boundedness Principle]{theorem:uniform-boundedness} implies that
By \autoref{proposition:bornological-continuous-complete} and \autoref{proposition:metrisable-bornological}, $E^*$ is a Banach space. The \hyperref[Uniform Boundedness Principle]{theorem:uniform-boundedness} implies that
\[
\sup_{A \in \cm}\norm{\mu(A)}_{E} = \sup_{A \in \cm}\norm{x_A}_{E^{**}} < \infty
\]