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Introduction. In measure theory and probability it is often useful to be able to extend a set function g to a measure p. One situation in which such an extension arises is that of obtaining limit measures for inverse (or projective) systems of measure spaces (,  ). Since such extensions do not exist in general, conditions must be placed on g in order to guarantee the existence of a measure which is an extension of g. A condition frequently assumed for this purpose is that g can bedoi:10.4153/cmb-1975-099-1 fatcat:okge2eofmzdt5jbxbkbgtbo7de