Week 1 Coursework Test
Due at 1600 on Tuesday 3rd October.
Prove that
Λ
(
Q
)
=
0
.
Let
X
be a non-empty set. Say that a subset
E
of
X
is
big
if
X
∖
E
is countable, and
small
if
E
is countable. Prove that
{
A
⊂
X
:
A
is small
}
∪
{
A
⊂
X
:
A
is big
}
is a σ-algebra on
X
.