### Questions (91)

 5 The inverse image of a measurable set under a measurable function is measurable? 3 Dilatation of a measurable set is a measurable set. 3 $\lim_{p\to r} \|f\|_p=\|f\|_r$ 2 Finding the symbol of an differential operator. 2 Problem 3. Page 240. Barry Simon. (Associated Lebesgue-Stieltjes measure )

### Reputation (513)

 +5 Sobolev imbedding theorem $H^{1,p}(\mathbb{R}^n)$ contained in $L^{{np}/(n-p)}(\mathbb{R}^n)$ (Taylor Michael) -2 Showing an inequality of a complex exponential function -6 Finding the derivative of $|x|^2:\mathbb{R}^n\to \mathbb{R}$ +5 Characteristic functions total in $L^2$?

### Answers (5)

 3 Showing affine transformations group generated by $2x$ and $x+1$ is the Baumslag-Solitar group. 1 Baumslag-Solitar Group $G=\langle a,t \mid tat^{-1}=a^k\rangle\cong\mathbb{Z}[1/k]\rtimes\langle t\rangle$? 0 Let $E$ be a subset of $\mathbb{R}$ with $m_*(E) > 0.$ There exists an open interval $I$ so that $m_*(E \cap I) \geq \alpha m_*(I).$ 0 Showing an inequality of a complex exponential function 0 Dilatation of a measurable set is a measurable set.

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 4 group-theory × 4 0 measure-theory × 36 3 group-presentation × 3 0 real-analysis × 28 3 affine-geometry × 2 0 functional-analysis × 26 1 geometric-group-theory × 2 0 hilbert-spaces × 9 1 abstract-algebra 0 lebesgue-integral × 8

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