ANISOTROPIC HARMONIC ANALYSIS ON HOMOGENEOUS TREES 5
is a uniquely determined finitely additive measure on £2.
Finally, in Chapter IV, we show that, with at most ten exceptions, the rep-
resentations
TTCT.TT^
and 7r7 are all irreducible. Next we show that these repre-
sentations are all inequivalent. Finally we show that if 7ra and TTS- are principal
series representations associated to two different random walks then ira and TTS-
are inequivalent.
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