The totality of permutations of K distinct numbers a1,...,aK, for varying a1,...,aK can be represented as a subset CK of Euclidean K-space RK, and the group G of Example 6.5.1 as the union of C2, C3, . . . . Let ν be the measure over G which assigns to a subset B of G the value ∞

k=2 µK(B ∩ CK),

where µK denotes Lebesgue measure in EK. Give an example of a set B ⊂ G and an element g ∈ G such that ν(B) > 0 but ν(Bg) = 0.
[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.]
Section 6.6