Remarks on the Geometry of Coordinate Projections in R
نویسندگان
چکیده
We study geometric properties of coordinate projections. Among other results, we show that if a body K ⊂ R 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.
منابع مشابه
Remarks on the Geometry of Coordinate Projections in Rn
We investigate some properties of coordinate projections. Among other results, we show that if a body K ⊂ Rn 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 a convex hull of a class of functions.
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