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Apr
20
awarded  Popular Question
Mar
9
answered An inequality about Lipschitz mapping and measurable sets in $\mathbb{R^{n}}$
Mar
9
comment An inequality about Lipschitz mapping and measurable sets in $\mathbb{R^{n}}$
So the issue with this approach is that if V is a very thin rectangle (some dimensions are small some are large), then your estimate on \|x-x_0\| is not so good because ``typical" points in your rectangle are far closer to the centre than your worst-case estimate. Instead, you can first prove the corresponding estimate for balls, and then try to use this together with the definition of the Lebesgue outer measure to complete your proof.
Mar
9
comment An inequality about Lipschitz mapping and measurable sets in $\mathbb{R^{n}}$
You should post the details of your construction of I'. We can say much more than that this product of intervals is bounded, we can put bounds on these intervals in terms of the Lipschitz constant and the size of the original intervals.
Mar
8
answered How to think about negative infinity in this limit $\lim_{x \to -\infty} \sqrt{x^2 + 3x} - \sqrt{x^2 + 1}$
Mar
8
revised Proof of a p-norm and Cauchy/Cauchy-Schwarz inequality generalization
deleted 2 characters in body
Mar
8
answered Proof of a p-norm and Cauchy/Cauchy-Schwarz inequality generalization
Mar
7
comment Bounded function approximated by simple function
We don't make any claim about uniform approximation, (although we get this in the bounded case), just about pointwise convergence. At what point $x\in(0,1]$ does my construction of $\phi_n$ fail to converge to $1/x$ ?
Mar
7
comment Bounded function approximated by simple function
Okay, well dropping $f$ measurable reduces the work, as our simple functions are then surely not required to be measurable simple functions. Boundedness certainly can be dropped. In taking the sum for $\phi_n$, we terminate at the first $k$ larger than $3^n$ for instance.
Mar
7
answered Bounded function approximated by simple function
Oct
9
awarded  Yearling
Jun
23
revised Evaluate: $\int_0^1 \frac{1-x}{(1+x)\log(x)}\, dx$
added 59 characters in body; edited title
Jun
23
asked Evaluate: $\int_0^1 \frac{1-x}{(1+x)\log(x)}\, dx$
Mar
6
comment Piecing together full density subsequences
Perfect, thank you! My attempts were along similar lines, but I missed the trick of working with complements (and the consequently logical choice for our $N_k$).
Mar
6
accepted Piecing together full density subsequences
Mar
6
asked Piecing together full density subsequences
Mar
3
awarded  Nice Answer
Jan
8
awarded  Tumbleweed
Oct
9
awarded  Yearling
Sep
24
awarded  Autobiographer