| Title:
|
On generalized “ham sandwich” theorems (English) |
| Author:
|
Golasiński, Marek |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
25-30 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let $A_1,\ldots ,A_m\subseteq \mathbb {R}^n$ be subsets with finite Lebesgue measure. Then, for any sequence $f_0,\ldots ,f_m$ of $\mathbb {R}$-linearly independent polynomials in the polynomial ring $\mathbb {R}[X_1,\ldots ,X_n]$ there are real numbers $\lambda _0,\ldots ,\lambda _m$, not all zero, such that the real affine variety $\lbrace x\in \mathbb {R}^n;\,\lambda _0f_0(x)+\cdots +\lambda _mf_m(x)=0 \rbrace $ simultaneously bisects each of subsets $A_k$, $k=1,\ldots ,m$. Then some its applications are studied. (English) |
| Keyword:
|
Lebesgue (signed) measure |
| Keyword:
|
polynomial |
| Keyword:
|
random vector |
| Keyword:
|
real affine variety |
| MSC:
|
12D10 |
| MSC:
|
14P05 |
| MSC:
|
58C07 |
| idZBL:
|
Zbl 1164.58312 |
| idMR:
|
MR2227109 |
| . |
| Date available:
|
2008-06-06T22:47:02Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107978 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
