# Tagged Questions

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### Uniform convex space

Please I want to know if this space $$H^1_{0,p}([0,+\infty))=\lbrace u, u\in AC([0,+\infty)), u(0)=u(+\infty)=0,\sqrt{p}u'\in L^2\rbrace$$ where $p>0$, $p\in L^1((0,+\infty))$ ...
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### Study of a function

I have this function $\displaystyle g(s)=\frac{s^{2-\sigma}}{1+s^2}, ~\text{for all} ~s\in \mathbb{R}$ , i need to find the interval of $\sigma$ and the maximum of the function $g$. I calculate the ...
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### a question about multivariable integral!

If $\lfloor x \rfloor$ denotes the greatest integer in $x$, evaluate the integral$$\iint_{R} \lfloor x+y \rfloor ~ \mathrm{d}x~ \mathrm{d}y$$where $R= \{(x,y)| 1\leq x\leq 3, 2\leq y\leq 5\}$. This ...
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### Consider the sequence ${f_n}$ with $n \ge 2$, defined on $[0,1]$ by
Consider the sequence ${f_n}$ with $n \ge 2$, defined on $[0,1]$ by f_n(x) = \left\{ \begin{array}{c} n^2x, &0 \le x \le \frac{1}{n} \\ 2n - n^2x, &\frac{1}{n} < x \le \frac{2}{n} \\ ...
Let $(X,\mathcal A)$ be a measurable space and let $f:X\to \mathbb R$ and $g:X\to \mathbb R$ be mesurable functions. Let $G$ be an open subset of $\mathbb R^2$. We want to show that \$\{x\in ...