PMATH 810, Winter 2015
Talk Topics
1. A simple proof of the existence of the Haar integral on locally compact
abelian groups. A. Izzo, Proc. Amer. Math. Soc., 115 (1992), no. 2,
581583.
2. Invariant measures on homogeneous spaces G/H (H non-normal). Reite

PMATH 950, Winter 2016
Assignment #3
Due: March 24.
Generally, G will denote a locally compact group, below.
1. Let G be compact and s G. Show that cfw_sn : n N is a subgroup of
G. Deduce that any closed subsemigroup of G is necessarily a subgroup.
2. Let

PMATH 950, Winter 2016
Assignment #2
Due: February 25.
Generally, G will denote a locally compact group, below.
1. Let N be a closed normal subgroup of G.
(a) Verify that the funtional on Cc (G) given by
Z
Z
I(f ) =
f (xn) dn dxN
G/N
N
where dn = dmN (n),

PMATH 950, Winter 2016
Assignment #1
Due: January 28.
Unless otherwise stated, (G, ) always denotes a Hausdorff locally compact group.
1. Show that (G, ) is complete in the following sense: If (x ) is a net in
G which satisfies the property that for every

Coures notes for PMATH 950
Christopher Hawthorne
Lectures by Nico Spronk, Winter 2016
Contents
1 Locally compact grapes
1
1
Locally compact grapes
We recall some topology.
Suppose X is a set. A topology on X is P(X) such that
, X .
If U, V then U V .
I