Gales and supergales are equivalent for defining constructive Hausdorff   dimension
  We show that for a wide range of probability measures, constructive gales are interchangable with constructive supergales for defining constructive Hausdorff dimension, thus generalizing a previous independent result of Hitchcock (cs.CC/0208043) and partially answering an open question of Lutz (cs.CC/0203017). 
Stephen A. Fenner