User Davide Giraudo - Mathematics Stack Exchange

247 votes

Accepted

Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$

answered Aug 9, 2012 at 17:03

219 votes

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Limit of $L^p$ norm

answered Nov 22, 2012 at 20:21

87 votes

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Monotone Convergence Theorem for non-negative decreasing sequence of measurable functions

answered Mar 24, 2012 at 20:05

81 votes

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Proof of Frullani's theorem

answered Sep 4, 2011 at 16:18

79 votes

Is there a bijective map from $(0,1)$ to $\mathbb{R}$?

answered Sep 21, 2012 at 8:21

77 votes

$L^p$ and $L^q$ space inclusion

answered Sep 20, 2011 at 11:35

74 votes

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Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?

answered Sep 24, 2011 at 15:09

61 votes

Accepted

Find the limit $\lim \limits_{n\to \infty }\cos \left(\pi\sqrt{n^{2}-n} \right)$

answered Jun 16, 2011 at 17:19

61 votes

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Is the product of two Gaussian random variables also a Gaussian?

answered Jan 21, 2012 at 21:22

58 votes

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Steinhaus theorem (sums version)

answered Nov 30, 2011 at 11:13

58 votes

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Bounded variation, difference of two increasing functions

answered May 5, 2012 at 11:44

53 votes

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"Every linear mapping on a finite dimensional space is continuous"

answered Feb 24, 2012 at 20:46

50 votes

Convergence of random variables in probability but not almost surely.

answered May 25, 2012 at 19:23

48 votes

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Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.

answered Feb 2, 2012 at 21:53

47 votes

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How to show path-connectedness of $GL(n,\mathbb{C})$

answered May 1, 2012 at 19:55

45 votes

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Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$

answered May 9, 2012 at 19:36

45 votes

Accepted

Prove the map has a fixed point

answered Mar 10, 2012 at 13:15

45 votes

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Approximating a $\sigma$-algebra by a generating algebra

answered Nov 4, 2012 at 17:27

36 votes

Derivative of convolution

answered Jul 31, 2012 at 16:57

35 votes

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Max dimension of a subspace of singular $n\times n$ matrices

answered Sep 23, 2011 at 12:01

33 votes

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Strong and weak convergence in $\ell^1$

answered Jun 1, 2011 at 18:37

31 votes

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Continuous functions on $[0,1]$ is dense in $L^p[0,1]$ for $1\leq p< \infty$

answered Oct 31, 2012 at 14:05

30 votes

Accepted

Matrix exponential convergence

answered Apr 12, 2012 at 19:49

29 votes

Number of $\sigma$ -Algebra on the finite set

answered May 11, 2012 at 8:42

29 votes

Accepted

Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$

answered Dec 31, 2011 at 0:08

29 votes

Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?

answered Jun 24, 2012 at 15:18

29 votes

Accepted

Convergence in measure of products

answered Jul 31, 2013 at 14:43

27 votes

Accepted

Another question on almost sure and convergence in probability

answered Oct 27, 2012 at 20:38

27 votes

Accepted

If a holomorphic function $f$ has modulus $1$ on the unit circle, why does $f(z_0)=0$ for some $z_0$ in the disk?

answered Apr 2, 2012 at 21:46

27 votes

Accepted

How to prove that an operator is compact?

answered Mar 2, 2012 at 23:00

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4,729 Answers

Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$

Limit of $L^p$ norm

Monotone Convergence Theorem for non-negative decreasing sequence of measurable functions

Proof of Frullani's theorem

Is there a bijective map from $(0,1)$ to $\mathbb{R}$?

$L^p$ and $L^q$ space inclusion

Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?

Find the limit $\lim \limits_{n\to \infty }\cos \left(\pi\sqrt{n^{2}-n} \right)$

Is the product of two Gaussian random variables also a Gaussian?

Steinhaus theorem (sums version)

Bounded variation, difference of two increasing functions

"Every linear mapping on a finite dimensional space is continuous"

Convergence of random variables in probability but not almost surely.

Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.

How to show path-connectedness of $GL(n,\mathbb{C})$

Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$

Prove the map has a fixed point

Approximating a $\sigma$-algebra by a generating algebra

Derivative of convolution

Max dimension of a subspace of singular $n\times n$ matrices

Strong and weak convergence in $\ell^1$

Continuous functions on $[0,1]$ is dense in $L^p[0,1]$ for $1\leq p< \infty$

Matrix exponential convergence

Number of $\sigma$ -Algebra on the finite set

Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$

Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?

Convergence in measure of products

Another question on almost sure and convergence in probability

If a holomorphic function $f$ has modulus $1$ on the unit circle, why does $f(z_0)=0$ for some $z_0$ in the disk?

How to prove that an operator is compact?