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Let $f:\mathbf R^n\to\mathbf R$ be a locally Lipchitz function. Denote $\mathrm H^n$ the $n$-dimensional Hausdorff measure. We know that for any $\mathrm H^n$-measurable subset $A\subset\mathbf R^n$, for $\mathcal{L}^1$-a.e. $t\in\mathbf R$, $A\cap f...

In 1966, Professor Michael Artin gave a course for first-year graduate students at MIT on commutative algebra. In that course he covered many classical topics, (the Spectrum of a commutative ring, localization, something about sheafs, stalks and exact...

This question relates a theory of Mosco convergence.
Let $X$ be a compact metric space, and $\mu$ a Borel measure on $X$.
A symmetric bilinear form $(\mathcal{E},\text{Dom}(\mathcal{E}))$ on $L^2(X,\mu)$ is called a Dirichlet form if the following conditions are satisfied:...

I learned about the fact that the automorphisms of $k[x,y]$ for a field $k$ are all tame and in fact composition of triangular and linear automorphisms. Then I saw the Nagata's example as a wild automorphism of $k[x][y,z]$. I am looking for some wild...