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Jan
21
awarded  Nice Question
Oct
12
asked how to prove this function is harmonic (Fritz John 4.1 #5)
Apr
8
comment Approximating measurable function by continuous ones
@GiuseppeNegro I did check on that one. But isn't regularity of the measure needed there?
Apr
8
revised Approximating measurable function by continuous ones
deleted 49 characters in body
Apr
8
comment Approximating measurable function by continuous ones
@DavideGiraudo Let's say $X$ is $\mathbb{R}^n$ with the usual topology. And sorry that I made a mistake in my original problem. I should ask for almost everywhere convergence.
Apr
8
comment Steiner symmetrization preserves area?
This is just by the construction of Steiner symmetric action and Fubini's theorem( where you can get: in order to get area, you integrate length of chords with respect to proper measure)
Apr
7
asked Approximating measurable function by continuous ones
Mar
13
awarded  Yearling
Feb
11
accepted Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
Feb
10
comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
I've actually been looking at this proof at a more careful level. And I realized Tubular Neighborhood and Retraction are exactly the tools that Lee used to solve the question I have. I guess I will choose @Potato as the best answer if nobody gives a better answer in the following couple of days! Thanks man, @Potato!
Feb
9
comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
I saw this proof before. But since I am not aware of Whitney approximation theorem or the smooth retraction mentioned in the proof, I skipped it. Bott, Tu's book's proof requires less background knowledge. But as I explained, I found I can't get around that point. I still wish that someone might be able to tell me how it is possible.
Feb
9
asked Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
Nov
20
awarded  Critic
Nov
20
awarded  Supporter
Nov
15
accepted Confused at the definition for integration of differential form over manifold
Nov
14
asked Confused at the definition for integration of differential form over manifold
Nov
13
comment How to prove this formula for Lie derivative for differential forms
@FlybyNight I believe $\phi_t$ in my notation is the $f$ in your notation. And $\phi_t^* w$, viewed as a whole thing, is exactly the $w^*$ in your notation. $\phi_t^*$ is the mapping that takes $ w$ to $w^*$. But never mind, I know how to prove this thing now. It's only a simple computation once you know what all those mappings really are. Thanks anyway.
Nov
13
revised How to prove this formula for Lie derivative for differential forms
edited body
Nov
13
comment How to prove this formula for Lie derivative for differential forms
@FlybyNight huh? $w$ here is a differential form.
Nov
12
asked How to prove this formula for Lie derivative for differential forms