It is known that all locally compact groups, and therefore compact groups, have a left-invariant Haar measure which is unique up to scalar constant, also a right-invariant one. Is there a strictly wider class of groups that has such a measure? What about weakening of these measures? What about hypergroups?


Thank you. HTTT.



To what extent has the Haar measure been generalized?
For general locally compact hypergroups, the existence of a Haar measure is still an open problem as far as I know. It has been answered affirmatively for Abelian, compact, or discrete hypergroups and those arising as coset spaces from locally compact groups. 


