Summary
Necessary and sufficient conditions are given for the existence of a finite measure which is equivalent to a given measure and invariant with respect to each transformation in a given commutative semigroup of measurable null-invariant point transformations. This result was already known for denumerably generated semigroups. A complementary result is proved which states that if one such equivalent measure exists, then there exists a unique equivalent measure which agrees with the original measure on the invariant sets.
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Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant No. AFOSR-68-1394.
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Hanson, D.L., Wright, F.T. On the existence of equivalent finite invariant measures. Z. Wahrscheinlichkeitstheorie verw Gebiete 14, 200–202 (1970). https://doi.org/10.1007/BF01111417
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DOI: https://doi.org/10.1007/BF01111417