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1d
comment Is proving $m(E) < \epsilon, \forall \epsilon > 0$ equivalent to prove $m(E) = 0$?
@DavidC.Ullrich That looks like an answer.
1d
comment Set-theoretic equality
The overlining is for the complementary set?
Jul
28
comment Residue integral: $\int_{- \infty}^{+ \infty} \frac{e^{ax}}{1+e^x} dx$ with $0 \lt a \lt 1$.
@tacos_tacos_tacos here is the same integral calculated using a rectangular contour.
Jul
26
revised Is there a proof for the maximum principle without the Cauchy integral theorem?
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Jul
26
revised A question about complex integration of $\frac{1}{p(z)}$
added 2 characters in body
Jul
26
answered A question regarding a proof in Ahlfors
Jul
26
answered Is there a proof for the maximum principle without the Cauchy integral theorem?
Jul
26
comment Is there a proof for the maximum principle without the Cauchy integral theorem?
@DanielFischer That's an answer :-)
Jul
26
comment A question about complex integration of $\frac{1}{p(z)}$
This is perfectly fine. And the reason why both integrals are equal is either by residues theorem or noting that those circles are homotopic.
Jul
26
comment Geometric mean never exceeds arithmetic mean
Which is in here
Jul
26
comment $|g(x)| \leq K \int_a^x|g| \ \ \forall x \in I$
See this answer.
Jul
25
comment Prove that a subset of a separable set is itself separable
That's not the case, $d(x_i,e_{(i,j)})\lt r_j$. And that's because each $e_{(i,j)}$ is choose to be a point of $B(x_i,r_j)$.
Jul
25
revised Prove that a subset of a separable set is itself separable
Being consistent with earlier notation.
Jul
25
comment Prove that a subset of a separable set is itself separable
@Wanderer Done.
Jul
25
revised Prove that a subset of a separable set is itself separable
added 327 characters in body
Jul
23
comment Some way to integrate $\sin(x^2)$?
Oh well it's concavity.
Jul
23
comment Some way to integrate $\sin(x^2)$?
How does one get the estimate $\cos\left(\frac\pi2 t\right)\geq 1-t$? Drawing the things it's obvious.
Jul
23
comment Integrating Fresnel Integrals with Cauchy Theorem?
possible duplicate of Some way to integrate $\sin(x^2)$?
Jul
22
revised Why if a function is holomorphic and injective in neighbourhood of $x_0$ then $f'(x)\ne 0$ in neighbourhood of $x_0$?
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Jul
21
revised Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
edited tags