Timeline for A measurable choice of inner-product preserving linear maps between two vector spaces
Current License: CC BY-SA 3.0
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| Aug 4, 2016 at 13:30 | comment | added | Uri Bader | After the current edit I would write my answer as follows: $TM$ is locally trivial, so find a measurable partition $\{U\}$ such that $TM|_U$ is trivial. Enough to work separately on each part, thus we can assume that $TU\simeq U\times \mathbb{R}^d$, and you have a measurable map $U\to$ inner products on $\mathbb{R}^d$. Take the standard basis of $\mathbb{R}^d$ at each $u\in U$ and form a Grahm-Schmidt process. You will obtain an orthonormal basis at each $u$ that varies measurably. Use it to form your linear map. | |
| Aug 3, 2016 at 14:54 | vote | accept | JustSomeGuy | ||
| Aug 3, 2016 at 13:59 | history | answered | Uri Bader | CC BY-SA 3.0 |