let (ω, "b", "λ") be the unit interval [0,1] with the lebesgue measure on borel sets. let μ be another measure on ω satisfying μ[("a","b")] = "b" − "a", and let "d" be the family of sets "s" such that μ[s] = λ[s]. let "i" = { ("a","b"),["a","b"),("a","b"],["a","b"] : 0 < "a" ≤ "b" < 1 }, and observe that "i" is closed under finite intersections, that "i" ⊂ "d", and that "b" is the σ-algebra generated by "i". it may be shown that "d" satisfies the above conditions for a dynkin-system. from dynkin's π-λ theorem it follows that "d" in fact includes all of "b", which is equivalent to showing that the lebesgue measure is unique on "b".