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April, 1970 A Remark on Almost Invariance
Robert H. Berk
Ann. Math. Statist. 41(2): 733-735 (April, 1970). DOI: 10.1214/aoms/1177697125


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.


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Robert H. Berk. "A Remark on Almost Invariance." Ann. Math. Statist. 41 (2) 733 - 735, April, 1970.


Published: April, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0218.62001
MathSciNet: MR253451
Digital Object Identifier: 10.1214/aoms/1177697125

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 2 • April, 1970
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