Timeline for Integration of differential forms using measure theory?
Current License: CC BY-SA 2.5
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| Jan 3, 2011 at 17:17 | comment | added | Deane Yang | An easy way to transfer all your knowledge about measures to the vector bundle setting is to observe that there is a natural way to map the space of sections of a vector bundle (equipped with a fibre metric) to the space of real-valued functions by simply mapping a section to its pointwise norm. You can then define the $L_p$ norm of a section to be the $L_p$ norm of its pointwise norm function. | |
| Jan 3, 2011 at 15:06 | comment | added | Dmitri Pavlov | @Meneldur: No, I don't have any reference for this. However, all hermitian vector bundles of dimension n over a measurable space are non-canonically isomorphic to the trivial vector bundle of dimension n. Thus the problem is reduced to the case of trivial vector bundles, provided that you check independence from the non-canonical isomorphism. The situation is similar to the case of differential operators over smooth manifolds: The most common case is the one of a differential operator from the trivial line bundle to itself, but often you need to consider arbitrary vector bundles. | |
| Jan 3, 2011 at 13:40 | history | edited | Meneldur | CC BY-SA 2.5 |
added 22 characters in body; added 58 characters in body
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| Jan 3, 2011 at 13:30 | history | answered | Meneldur | CC BY-SA 2.5 |