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We provide a new proof of a theorem whose proof was sketched by Sullivan('82), namely that if the Poincar\'e exponent of a geometrically finiteKleinian group $G$ is strictly between its minimal and maximal cusp ranks, thenthe Patterson--Sullivan measure of $G$ is not proportional to the Hausdorff orpacking measure of any gauge function. This disproves a conjecture of Stratmann('97, '06).

On interpreting Patterson--Sullivan measures of geometrically finite groups as Hausdorff and packing measures