The problem asks whether the decomposition of invariant measures on definable groups in NIP theories into idempotent components can be made canonical and natural. More precisely, when a definable group G in a NIP structure carries an invariant Keisler measure, one wants to know if there is a systematic, choice-free way to break that measure into idempotent pieces that respects the algebraic structure and behaves predictably under maps between groups. The idempotent measure conjecture proposes that every invariant measure is a combination of idempotent ones, but the question of whether such a decomposition can be made functorial remains unresolved.