Re: Winternitz Theorem

From: Dan Luecking (Look-In-Sig_at_uark.edu)
Date: 09/25/04 

Date: Sat, 25 Sep 2004 14:30:03 +0000 (UTC)

On Fri, 24 Sep 2004 14:00:06 +0000 (UTC), Gerry Myerson
<gerry@maths.mq.edi.ai.i2u4email> wrote:

>In article <civrim$kmg$1@news.ks.uiuc.edu>,
> andreas wagener <108076@gmx.net> wrote:
>
>
>Here's something from Math Reviews that may be of use.
>
>MR1099773 (92e:52010)
> Scott, P. R.(5-ADLD)
> On the union of convex bodies with no interior point in common.
> Mathematika 37 (1990), no. 2, 245--250.
>52A35 (52A20)
>
>  Let $K_1,\cdots,K_{d+1}$ be $d+1$ convex bodies in $d$-dimensional
>Euclidean space which have no interior point in common. The author shows
>that $m(\bigcup_iK_i)\geq C_d\min_jm(K_j)$, where $i$ and $j$ vary from
>$1$ to $d+1$, $C_d$ is a constant depending only on the dimension and
>$m(·)$ is the measure of the set.

Am I missing something? How is this not trivial with $C_d = d+1$?

Dan 

-- 
Dan Luecking                     Department of Mathematical Sciences
University of Arkansas           Fayetteville, Arkansas 72701
To reply by email, change Look-In-Sig to luecking

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