Let ( = {1, 2, 3, 4}, let C = {(, {1, 2},{1, 2},{2, 4},{ 3, 4},

Let ( = {ω1, ω2, ω3, ω4}, let C = {(, {ω1, ω2},{ω1, ω2},{ω2, ω4},{ ω3, ω4}, (, and define μ on C as follows:
μ({ω1, ω2}) = μ ({ω1, ω3}) = μ ({ω1, ω4}) = μ ({ω3, ω4}) = 3, μ (() = 6, μ (() = 0.
Next, on P((), define the measures μ1 and μ2 by taking
μ1({ω1}) = μ1 ({ω4}) = μ2 ({ω2}) = μ2 ({ω3}) = 1,
μ1({ω2}) = μ1 ({ω3}) = μ2 ({ω1}) = μ2 ({ω4}) = 2,
Then show that
(i) C is not a field.
(ii) μ is a measure on C.
(iii) Both μ1 and μ2 are extensions of μ (from C to P(()).
(iv) Construct the outer measure μ* (as is defined in Definition 5) by means of μ defined on C.
(v) Conclude that μ* ( μ1 ( μ2 (so that, if the class C is not a field, the extension of (even a finite measure μ on C) need not be unique.