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A general Hobby-Rice Theorem and cake cutting |
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| Authors: | Daniel Wulbert |
| Institution: | (1) Mathematics Department 0112, University of California, San Diego, 92093 La Jolla, CA, USA |
| Abstract: | LetX be a Borel subset of a separable Banach spaceE. Letμ be a non-atomic,σ-finite, Borel measure onX. LetG ⊆L
1 (X, Σ,μ) bem-dimensional.
Theorem:There is an l ∈ E* and real numbers −∞=x
0<x
1<x
2<…<x
n<x
n+1=∞with n≤m, such that for all g ∈ G,
![$$\sum\limits_{i = 0}^n {\left( { - 1} \right)^i } \int {_{X \cap l^{ - 1} \left {x_i ,x_i + 1} \right]} ^{g d\mu = 0} } $$](/content/h2p4397m17416128/11856_2007_Article_BF02784162_TeX2GIFIE14.gif) |
| Keywords: | |
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