Abstract
In [1], P. J. Bickel and the author presented a theorem giving sufficient conditions for the equivalence of invariant and almost-invariant functions. In the subsequent discussion, it was intimated without proof that the results extend to certain other classes of distributions that do not satisfy the hypotheses of the main theorem. A small lacuna was glossed over in the discussion; however, the conclusions are correct for the examples given there. In this note we justify those conclusions. We adopt the notation of [1] without further comment.
Citation
Robert H. Berk. "A Remark on Almost Invariance." Ann. Math. Statist. 41 (2) 733 - 735, April, 1970. https://doi.org/10.1214/aoms/1177697125
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