All Questions
155 questions
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Dense Egoroff theorem
Suppose that $f_n:X\rightarrow V$ is a sequence of continuous functions from a compact metric space $X$ to a Banach space $V$ and let $\mu$ be a Radon measure on $X$ and $\epsilon>0$ be given.
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- 5,405
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1
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113
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Verifying that a map to $L^2_{\text{loc}}$ is continuous
Let $M$ be a smooth manifold on which a Lie group $G$ acts properly, such that the orbit space $M/G$ is compact. Suppose $c:M\rightarrow [0,\infty)$ is a compactly supported smooth function with the ...
- 1,903
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63
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The union of weighted compact supported continuous function
Let $\Omega\subset \mathbb R^N$ be open. Given a weight function $v\geq 1$ such that $v\in L^1_{\text{loc}}(\Omega)$ and $l.s.c$. Also supposethere exists a Lipschitz continuous sequence $v_n$ such ...
- 679
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405
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Dual of the space of vector valued Borel measures
What is the dual of the space of all vector valued Borel measures?
- 21
-1
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1
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114
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Interpolation inequality $\int_{\mathbb R} u^3 dx \le \int_{\mathbb R} (u')^2 dx + \int_{\mathbb{R}} u^2 dx$ [closed]
Let $u \in C^\infty(\mathbb R)$. Is it true that the following interpolation inequality holds?
$$\int_{\mathbb R} u^3 dx \lesssim \int_{\mathbb R} (u')^2 dx + \int_{\mathbb{R}} u^2 dx$$
- 217