75. The totality of permutations of K distinct numbers al"' " a K for varying a., • . . , aK can be represented as a subset CK of Euclidean K-space RK, and the group G of Example 8 as the union of C2 , C3 , • •• • Let I' be the measure over G which assigns to a subset B of G the value Er_2 J.L K(B () CK), where J.LK denotes Lebesgue measure in EK • Give an example of a set BeG and an element g E G such that I'(B) > 0 but I'(Bg) = O. [If

a, b,

c, d are distinct numbers, the permutations g, g' taking (a ,

b) into (b,a) and

(c,

d) into

(d,

c) respectively are points in C2 , but gg' is a point in C4 · ]