Abstract
We study the Fuglede p-modulus of a certain family of measures \(\Sigma \). These measures are push-forward measures of a certain fixed measure. We show the existence of a natural family of measures \({\mathcal {T}}\) associated with \(\Sigma \). We study the possibility of the equality of p-moduli of these two families.
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References
Ambrosio, L., Di Marino, S., Savaré, G.: On the duality between \(p\)-modulus and probability measures. J. Eur. Math. Soc. (JEMS) 17(8), 1817–1853 (2015)
Badger, M.: Beurling’s criterion and extremal metrics for Fuglede modulus. Ann. Acad. Sci. Fenn. Math. 38(2), 677–689 (2013)
Bogachev, V.I.: Measure Theory, vol. 2. Springer, Berlin (2007)
Fuglede, B.: Extremal length and functional completion. Acta Math. 98, 171–219 (1957)
Kalina, J., Pierzchalski, A.: A variation of the modulus of submanifold families. In: Analytic Functions, Kozubnik 1979 (Proceedings of the Seventh Conference, Kozubnik), pp. 250–257. Lecture Notes in Math., 798. Springer, Berlin (1979)
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I wish to thank the anonymous referee for the careful reading of the manuscript and suggested improvements.
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Ciska-Niedziałomska, M. Measure families with the same Fuglede p-modulus. Arch. Math. 119, 63–74 (2022). https://doi.org/10.1007/s00013-022-01735-z
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DOI: https://doi.org/10.1007/s00013-022-01735-z