Abstract
We study ergodic infinite measure preserving transformations T possessing reference sets of finite measure for which the set of densities of the conditional distributions given a first return (or entrance) at time n is precompact in a suitable function space. Assuming regular variation of wandering rates, we establish versions of the Darling-Kac theorem and the arcsine laws for waiting times and for occupation times which apply to transformations with indifferent orbits and to random walks driven by Gibbs-Markov maps.
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