This paper argues that Basque non-agreeing quantifiers are conceptually measures and that measures head their own functional projection in the expanded structure of the Noun Phrase. This functional projection is placed in between the Classifier Phrase (where division occurs) and the Number Phrase (where counting occurs), following Borer (2005). The authors also show that non-agreeing quantifiers are sensitive to the nature of the predicates they associate to. Non-agreeing quantifiers seem to measure both individuals and events/states, as long as the latter denote non-trivial part-whole structures. The predicate sensitivity of non-agreeing quantifiers, the authors claim, has two sources: (i) the monotonicity constraint (Schwarzschild, 2002); (ii) a homomorphism relation (Krifka, 1989; Filip, 1996; Nakanishi, 2004, 2007) which maps the denotation of a noun phrase into the denotation of the predicate. The predicate sensitivity of non-agreeing quantifiers can thus be viewed as the result of this mapping relation.