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 w, there exists a subset of the cake that all people value at exactly a fraction w of the total cake value, and it can be cut using at most
[1] 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
If the cake is not circular (that is, the endpoints are not identified), then
be the subset of all weights for which the theorem is true.
In other words, the theorem is valid for every possible weight.
Stromquist and Woodall prove that the number
is tight if the weight
is either irrational, or rational with a reduced fraction