From a measure space, (X, μ𝕏) we define a measure μ ℙ(𝕏) on the power set of X. If (X,τ) is a compactum, whose topology τ is compatible with the measure μ𝕏 on X, then the measure μ ℙ(𝕏) restricts to a natural measure on the hyperspace of closed sets of that given compactum. Surprisingly, under very mild conditions, μℙ(𝕏) is always supported on the hyperspace of finite subsets.