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Results tagged with real-analysis
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user 4281
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
5
votes
1
answer
135
views
Reference for higher order Campanato Lemmas, e.g. `Sufficiently fast L^2 decay on balls to a...
Whence can I reference the following fact (I have seen it quoted as `standard' in respectable places, so I hope it is so)?:
Let $f : B_2(0) \to \mathbb{R}$, say $f \in L^2(B_2(0))$ . Suppose that the …
- 1,771
0
votes
0
answers
102
views
Must the Lebesgue measure of a $\rho$ - neighbourhood of an $(n-2)$ - dimensional set be at ...
The Lebesgue measure of a $\rho$-neighbourhood of a point in $\mathbb{R}^2$ is of course equal to $c\rho^2$. Similar such considerations in higher dimensions lead me to the following question:
Given …
- 1,771
12
votes
Taking "Zooming in on a point of a graph" seriously
As Rbega says in the comments, if you are really keen to see this rescaling idea put to use in a more rigorous or advanced way, then you can look at some Geometric Measure Theory. While it will look v …
- 1,771
7
votes
4
answers
6k
views
The characteristic (indicator) function of a set is not in the Sobolev space H¹
Is it true that the characteristic
(indicator) function of a subset of
Euclidean space with finite positive
measure is never in the Sobolev space
$H^1 = W^{1,2}$? And if so, what is the best/easiest/ …
- 1,771