Exercise 3, § 1

Integration, VII

Let G be a locally compact group, $\mu$ a left Haar measure on G, and $\nu = \Delta_G^{-1/2} \cdot \mu$ . Show that

\gamma(s)\nu = \Delta_G(s)^{1/2}\nu, \quad \delta(s)\nu = \Delta_G(s)^{1/2}\nu, \quad \dot{\nu} = \nu.

Solution

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