Corollary 2

Every relatively left-invariant measure is relatively right-invariant.

For, with the notations of Cor. 1,

On account of Cor. 2, we shall henceforth speak of relatively invariant measures on G, without further specification. The relatively invariant measures admit as special cases the left Haar measures and the right Haar measures. Given a relatively invariant measure $\nu$ on G, it is convenient to distinguish between its left multiplier $\chi$ and its right multiplier $\chi'$, defined by $\gamma(s)\nu = \chi(s)^{-1}\nu$, $\delta(s)\nu = \chi'(s)\nu$. By (34), these multipliers satisfy the relation

Still denoting by $\mu$ a left Haar measure, we have

thus $\nu'$ is relatively invariant with left multiplier $\chi^{-1} \Delta_G^{-1}$ and right multiplier $\chi^{-1}$.

The concepts of negligible, locally negligible, measurable and locally integrable function are the same for every relatively invariant measure.