Ergodic theorem for groups?

Does anyone know of a proof of the following under some conditions?

If we have a sequence of random variables Xi representing a random walk
on a finite group G, and a function f on G, will the 'time average'

n
1/n sum( f( Xi ) )
i=1

converge a.e. to the 'expectation' of f on G, calculated with the
constant distribution

1/|G| sum( f( g ) )
g in G

I can't seem to find this anywhere, though it may be well known for all
I know.

Thank you for your help,
Dan

.

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