Remarks on the geometry of coordinate projections in ℝ n

S. Mendelson; R. Vershynin

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Remarks on the geometry of coordinate projections in ℝ n

机译：ℝn 中有关坐标投影的几何的注释

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We study geometric properties of coordinate projections. Among other results, we show that if a bodyK⊂ℝ n has an “almost extremal” volume ratio, then it has a projection of proportional dimension which is close to the cube. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.

机译：我们研究坐标投影的几何特性。在其他结果中，我们表明，如果bodyK⊂ℝn 具有“几乎极值”的体积比，则它的比例投影将接近于立方体。我们还根据类本身的崩溃维度，对一类函数的凸包的崩溃维度进行了清晰的估计。

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《Israel Journal of Mathematics》 |2004年第1期|203-220|共18页
作者
S. Mendelson; R. Vershynin;
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作者单位

Research School of Information Sciences and Engineering The Australian National University;

Department of Mathematics University of California Davis;

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7. Remarks on the geometry of coordinate projections in R^n [O] . Mendelson, S., Vershynin, R. 2003

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Remarks on the geometry of coordinate projections in ℝ n

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