Absolute continuity and uniqueness of measures on metric spaces
HTML articles powered by AMS MathViewer
- by Pertti Mattila PDF
- Trans. Amer. Math. Soc. 266 (1981), 233-242 Request permission
Abstract:
We show that if two Borel regular measures on a separable metric space are in a suitable sense homogeneous, then they are mutually absolutely continuous. We use such absolute continuity theorems together with some density theorems to prove the uniqueness of measures more general than Haar measures.References
- Jens Peter Reus Christensen, On some measures analogous to Haar measure, Math. Scand. 26 (1970), 103–106. MR 260979, DOI 10.7146/math.scand.a-10969
- Jessie Ann Engle, A $5-r$ uniqueness theorem, Trans. Amer. Math. Soc. 201 (1975), 89–104. MR 355009, DOI 10.1090/S0002-9947-1975-0355009-3
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- Pertti Mattila, Differentiation of measures on uniform spaces, Measure theory, Oberwolfach 1979 (Proc. Conf., Oberwolfach, 1979) Lecture Notes in Math., vol. 794, Springer, Berlin, 1980, pp. 261–283. MR 577976
- E. J. Mickle and T. Radó, A uniqueness theorem for Haar measure, Trans. Amer. Math. Soc. 93 (1959), 492–508. MR 109852, DOI 10.1090/S0002-9947-1959-0109852-7
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 266 (1981), 233-242
- MSC: Primary 28A12; Secondary 28A15
- DOI: https://doi.org/10.1090/S0002-9947-1981-0613793-8
- MathSciNet review: 613793