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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

2 votes
1 answer
273 views

A question about box dimension and Hölder condition

It is known that if a real continuous function $f(x)$ satisfies a local $\alpha$-Hölder condition on a closed interval $[a,b]$, the box dimension of the graph of $f(x)$ on $[a,b]$ will be not greater …
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1 vote
2 answers
226 views

A question about dense sets

Suppose that $A$ is a given subset of $I=[0,1],\ $ and $ \left\{ x_j = \frac{j}{m} \right\}_{j=0}^{m}\ $ is the $m$-partition of $I$, and $\nu(m)$ is the number of $\ [x_{i-1},x_{i}]\ $ such that $\ [ …
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  • 419