Last Updated：2026/01/01
Sentence
Indeed,
if
there
is
one
property
of
locally
compact
groups
more
responsible
than
any
other
for
the
rich
positive
content
of
their
representation
theory,
it
is
their
possession
of
left-invariant
and
right-invariant
(Haar)
measures.
The
connection
between
the
representation
theory
of
a
locally
compact
group
and
that
of
general
Banach
algebras
proceeds
directly
from
Lebesgue
integration
with
respect
to
Haar
measure
on
the
group.
Quizzes for review
Indeed, if there is one property of locally compact groups more responsible than any other for the rich positive content of their representation theory, it is their possession of left-invariant and right-invariant (Haar) measures. The connection between the representation theory of a locally compact group and that of general Banach algebras proceeds directly from Lebesgue integration with respect to Haar measure on the group.
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