This preview shows page 1. Sign up to view the full content.
Analysis 2
Homework 04
1. For
A
⊂
N
=
{
1
,...
} 3
n
let
ν
n
(
A
) =
1
n
μ
#
(
A
∩
[1
,n
]);
let
C
denote the collection of those subsets
A
for which (
ν
n
(
A
))
∞
n
=1
converges
and deﬁne
ν
:
C →
[0
,
1] :
A
7→
lim
n
→∞
ν
n
(
A
)
.
Is (
N
,
C
,ν
) a probability space?
2. Let
R
be equipped with the Borel
σ
algebra. Recall that every
continuous
function from
R
to itself is (Borel) measurable. Is every (weakly) monotonic
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/08/2011 for the course MHF 3202 taught by Professor Larson during the Spring '09 term at University of Florida.
 Spring '09
 LARSON

Click to edit the document details