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Results tagged with measure-theory
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user 129565
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
0
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Borel sets and Method I measure
If $(X,d)$ is a metric space, say a function $\tau$ on some class $\mathscr{C}$ of subsets of $X$ is a pre-measure, if $\emptyset \in \mathscr{C}$, $\tau(\emptyset)=0$ and $0\le \tau(C)\le +\infty$ f …
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Does Ahlfors–David regularity of a measure imply its Fourier asymptotic behavior?
Let $\mu$ be a Borel probability measure on $R^d$. If $\mu$ satisfies $\mu(B(x,r))\le Cr^\alpha$ for any $x\in R^d$ and $r>0$, then Strichartz (Fourier asymptotics of fractal measures, J. Funct. Anal. …
- 207
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1
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How to check that the surface measure is the weak limit of $\delta^{-1}\mathcal{L}^n|_{B(0,1...
We denote the unit sphere $\{x\in\mathbb{R}^n:|x|=1\}$ by $S^{n-1}.$ If $x\in\mathbb{R}^n\setminus\{0\}$, the polar coordinates of $x$ are
\begin{align*}
r=|x|\in(0,\infty),\quad \gamma=\dfrac x{| …
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