"Haar measures" on CGWH groups?

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Is there a suitable notion of "Haar measure" on CGWH groups (topological groups whose topology is compactly generated weak Hausdorff)? I know that if a topological group admits a Haar measure, then it should be locally compact. So a Haar measure does not exist in general CGWH groups. But what if we weaken the regularity properties? Does CGWH groups have a unique (up to scaling) translation invariant measure satisfying certain (weaker) regularities?