Unimodular group

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This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)
View a complete list of such properties

Definition

A unimodular group is a locally compact group satisfying the following equivalent conditions:

  1. Every left Haar measure is a right Haar measure.
  2. Every right Haar measure is a left Haar measure.
  3. There is a bi-invariant Haar measure on the group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
locally compact abelian group |FULL LIST, MORE INFO
compact group |FULL LIST, MORE INFO
discrete group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
locally compact group