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luka5z's user avatar
luka5z
  • Member for 10 years, 5 months
  • Last seen more than 5 years ago
28 votes
2 answers
16k views

Every weakly convergent sequence is bounded

22 votes
1 answer
6k views

Fubini's theorem for conditional expectations

21 votes
1 answer
23k views

Prove multi-dimensional Mean Value Theorem

14 votes
1 answer
10k views

Prove that $C^1[0,1]$ is not complete with norms [duplicate]

13 votes
1 answer
8k views

Calculate integral $\int_0^1 e^{e^{e^x}} dx$

12 votes
2 answers
6k views

Integrating around simple pole and semicircle

11 votes
3 answers
375 views

Prove that $f_n(x)=\frac{x}{n}$, $n=1,2,\ldots$ does not converge uniformly on $\mathbb{R}$

10 votes
1 answer
761 views

Prove that if $a_1 + a_2 + \ldots$ converges then $a_1+2a_2+4a_4+8 a_8+\ldots$ converges and $\lim na_n=0$

10 votes
3 answers
2k views

Why unit open ball is open in norm topology, but not open in weak topology?

10 votes
2 answers
4k views

Lebesgue integral and absolute value

9 votes
1 answer
3k views

Function holomorphic except for real line and continuous everywhere is entire

9 votes
6 answers
4k views

Intuition behind Chebyshev's inequality

8 votes
1 answer
4k views

$\ell^{\infty}(\mathbb N)$ is not a separable space

7 votes
1 answer
12k views

Prove the scaling property of a Brownian motion.

7 votes
2 answers
2k views

Dense subspace of linear space and functional equal to $0$

7 votes
3 answers
11k views

Pole on a contour. Problem with integration

7 votes
1 answer
678 views

Prove that $\int_a^b \left( \int_c^d f(x,y)dy\right) dx=\int_c^d \left( \int_a^b f(x,y)dx\right) dy$

7 votes
1 answer
3k views

Lebesgue measure vs Lebesgue-Stieltjes measure

6 votes
2 answers
4k views

Prove that if the sequence of increasing functions $(f_n)$ converges to $f$, then $f$ is increasing

6 votes
3 answers
918 views

Give another proof of intermediate value theorem

6 votes
1 answer
1k views

Continuous map $\mathbb{R}^n\rightarrow\mathbb{R}^n$

6 votes
2 answers
407 views

Not sure about the derivative of the integral

6 votes
2 answers
573 views

Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$? [duplicate]

5 votes
2 answers
3k views

Prove that integral is a Gaussian random variable, compute its mean and variance

5 votes
2 answers
192 views

Solve complex equation with exponential

5 votes
1 answer
181 views

What does $\overline{z}\mathbb{1}$ and $\underline{z}\mathbb{1}$ mean?

5 votes
1 answer
5k views

Show that one-sided limits always exist for a monotone function (on an interval)

5 votes
1 answer
808 views

Find all holomorphic functions $f$ satisfying $f(1-f(z))=f(z)$?

5 votes
0 answers
184 views

Show that if $f$ is measurable then $\{x\in A:c=f(x)\}$ is measurable for each $c$.

5 votes
1 answer
4k views

Prove that $\int_0^1 f(x)dx=0$ if $f(\frac{1}{n})=1$ for $n=1,2,3,\ldots$ and $f(x)=0$ for all other $x$

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