A polyomino with no stochastic function (Q762170)

A polyomino P is defined to be a finite subset of the set S of unit squares with integer vertices in \(R^ 2\). A rectangle \(R^*\) of P is maximal if it is not properly contained in another rectangle of P. A function f from P to the non-negative reals is called a stochastic function if, for every maximal rectangle \(R^*\) of P, \(\sum_{s\in R^*}f(s)=1.\) In this paper the authors provide an example of a polyomino P which admits no stochastic function.