Published online by Cambridge University Press: 12 March 2014
T.K. Menas [4, pp. 225–234] introduced a combinatorial property Χ(μ) of a measure μ on a supercompact cardinal κ and proved that measures with this property also have the partition property. We prove here that Menas' property is not equivalent to the partition property. We also show that if a is the least cardinal greater than κ such that Pκα bears a measure without the partition property, then α is inaccessible and -indescribable.