# Romeo

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"If you want to build a ship, don't drum up the men to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea." (Antoine de Saint ExupĂ©ry)

"Borders? I have never seen one. But I have heard they exist in the minds of some people." (Thor Heyerdahl)

"We are not now that strength which in old days \ moved earth and heaven, that which we are, we are, \ One equal temper of heroic hearts,\ Made weak by time and fate, but strong in will \ To strive, to seek, to find, and not to yield." (Alfred Tennyson)

# 94 Questions

 18 If $\int_{\mathbb R^2} \frac{\vert f(x)-f(y)\vert}{\vert x-y\vert^2}dxdy<+\infty$ then $f$ is a.e. constant 14 If $\lim_n f_n(x_n)=f(x)$ for every $x_n \to x$ then $f_n \to f$ uniformly on $[0,1]$? 12 Does $f_n \to 0$ in $L^1(\mathbb R^2)$ imply that $f_{n_k}(x,\cdot)\to 0$ in $L^1(\mathbb R)$ for almost every $x \in \mathbb R$? 10 A trigonometric series 8 Does $f\colon \Omega \to \mathbb R$ differentiable imply $f$ locally Lipschitz?

# 2,468 Reputation

 +5 Do the radii of a family of nested balls (in a Banach space) converge? +5 Boundness of solutions of $x'+x+f(x)=0$ +10 Convergence of $\sum_{n=2}^\infty \frac{1}{n^\alpha \ln^\beta (n)}$ +5 Smooth structure on the set of all straight lines

 11 How to prove $n^5 - n$ is divisible by 30 without reduction 6 Convergence of $\sum_{n=2}^\infty \frac{1}{n^\alpha \ln^\beta (n)}$ 5 Show harmonic function is constant on $\mathbb{R}^n$ 4 a problem on uniform continuity 4 Show that a finite-dimensional Banach space has a bijective compact operator

# 92 Tags

 19 real-analysis × 40 6 banach-spaces × 5 14 sequences-and-series × 14 6 pde × 4 11 elementary-number-theory 5 measure-theory × 15 9 convergence × 10 5 limits × 4 7 functional-analysis × 16 5 harmonic-functions × 2

# 4 Accounts

 Mathematics 2,468 rep 2527 Area 51 151 rep 2 German Language 103 rep 114 TeX - LaTeX 101 rep 2