Pedro Gomes's user avatar
Pedro Gomes's user avatar
Pedro Gomes's user avatar
Pedro Gomes
  • Member for 5 years, 9 months
  • Last seen this week
38 votes
6 answers
29k views

Infimum and supremum of the empty set

31 votes
2 answers
13k views

$\mathbb{R}$ with the lower limit topology is not second-countable

31 votes
2 answers
17k views

Uniform convergence of derivatives, Tao 14.2.7.

28 votes
1 answer
13k views

$\ell_p$ is Hilbert if and only if $p=2$

  • 1,763
27 votes
2 answers
10k views

Taylor's Theorem with Peano's Form of Remainder

  • 80.4k
26 votes
2 answers
10k views

Is complex conjugation needed for valid inner product?

  • 812
25 votes
2 answers
8k views

Inducing orientations on boundary manifolds

21 votes
2 answers
26k views

Cartesian product of compact sets is compact

12 votes
1 answer
3k views

Compact $\omega$-limit set $\Rightarrow$ connected

  • 1,117
11 votes
2 answers
2k views

Orientability of a product of smooth manifolds implies orientability of each factor

  • 2,580
9 votes
1 answer
6k views

Expectation of Exponential of Stochastic Integral

  • 9,125
8 votes
2 answers
4k views

The space of sequences as a complete metric space

  • 1,201
8 votes
4 answers
5k views

Are $\emptyset$ and $X$ closed, open or clopen?

  • 3,427
7 votes
2 answers
2k views

Natural projection of tangent bundle is submersion

  • 684
7 votes
3 answers
5k views

Is $\sin^2x$ uniformly continuous on$x\in [0,\infty]$

  • 1,436
7 votes
2 answers
4k views

Show that $X$ is Hausdorff if and only if the diagonal $\Delta = \{(x, x):x \in X\}$ is closed in $X \times X$ [duplicate]

  • 1,978
7 votes
2 answers
8k views

Is the lower limit topology finer than the standard topology on $\mathbb{R}$?

  • 8,658
6 votes
1 answer
2k views

Understanding Mobius bundle.

6 votes
1 answer
267 views

$(\int f(x,y)\lambda(dy))^{-1}$ is a density of the absolutely continuous part of Lebesgue measure w.r.t. $P_X$?

6 votes
1 answer
248 views

Doubt about the convergence of $\displaystyle \sum_k^{n-1}f(\frac{k+\theta} n)-n\int_0^1 f(x)\,dx$

  • 4,245
6 votes
1 answer
2k views

Showing that the Lebesgue-Stieltjes measure is absolutely continuous with respect to Lebesgue measure (and one more thing).

  • 1,966
6 votes
2 answers
5k views

continuous image of a locally compact space is locally compact

  • 29.7k
6 votes
2 answers
7k views

Uniform distribution on unit disk

  • 443
5 votes
1 answer
973 views

Linear Transformation from Infinite dimensional to Finite dimensional Space

  • 18.4k
5 votes
1 answer
244 views

Variance of the square variation process

  • 1,567
5 votes
1 answer
3k views

show that the solution is a local martingale iff it has zero drift

  • 2,880
5 votes
2 answers
541 views

Proving Bishop's Theorem using Krein-Milman Theorem

  • 2,351
4 votes
1 answer
313 views

Ex 10.2.1 in Klenke's Probability Theory textbook

4 votes
3 answers
198 views

Compute $\lim_{n\to\infty}\int_\limits{0}^{\infty}\frac{dx}{x^{n}+1}$

  • 4,245
3 votes
0 answers
146 views

Proving a prior distribution defined by a trignometric basis on $L^2(\mathbb{T})$ is Hölder continous

  • 4,245