For an arbitrary set ( containing at least two points, consider the trivial field F = {(, (}, and let (the finite measure) be

For an arbitrary set ( containing at least two points, consider the trivial field F = {(, (}, and let (the finite measure) μ be defined on F by: μ (() = 0 and μ (() =1.
(i) Determine the set function μ* on P((), as is given in the definition just prior. (Which μ* is, actually, an outer measure)
(ii) Show that the σ-field of μ*-measureable sets, A*, say, is the trivial σ-field, so that A* is strictly contained is P(().