About: Stromquist–Woodall theorem

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The Stromquist–Woodall theorem is a theorem in fair division and measure theory. Informally, it says that, for any cake, for any n people with different tastes, and for any fraction r, there exists a subset of the cake that all people value at exactly a fraction r of the total cake value. The theorem is about a circular 1-dimensional cake (a "pie"). Formally, it can be described as the interval [0,1] in which the two endpoints are identified. There are n continuous measures over the cake: ; each measure represents the valuations of a different person over subsets of the cake.

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  • The Stromquist–Woodall theorem is a theorem in fair division and measure theory. Informally, it says that, for any cake, for any n people with different tastes, and for any fraction r, there exists a subset of the cake that all people value at exactly a fraction r of the total cake value. The theorem is about a circular 1-dimensional cake (a "pie"). Formally, it can be described as the interval [0,1] in which the two endpoints are identified. There are n continuous measures over the cake: ; each measure represents the valuations of a different person over subsets of the cake. The theorem says that, for every weight , there is a subset , which is a union of at most intervals, which all people value at exactly : (en)
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  • The Stromquist–Woodall theorem is a theorem in fair division and measure theory. Informally, it says that, for any cake, for any n people with different tastes, and for any fraction r, there exists a subset of the cake that all people value at exactly a fraction r of the total cake value. The theorem is about a circular 1-dimensional cake (a "pie"). Formally, it can be described as the interval [0,1] in which the two endpoints are identified. There are n continuous measures over the cake: ; each measure represents the valuations of a different person over subsets of the cake. (en)
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  • Stromquist–Woodall theorem (en)
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