Abstract
We give an example showing that the uniformly bounded variation condition in the compactness theorem of Góra and Boyarsky [ Canad. J. Math. 41 (1989), 855-869] is crucial for L 1 stability of an absolutely continuous invariant measure (acim) of a piecewise expanding transformation. The same example shows that a simple method of approximating an invariant density of a piecewise expanding transformation can give the wrong results.
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