Sean Gomes
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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