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Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampère equation

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Abstract

We prove that having a quasi-metric on a given set X is essentially equivalent to have a family of subsets S(x, r) of X for which y∈S(x, r) implies both S(y, r)⊂S(x, Kr) and S(x, r)⊂S(y, Kr) for some constant K. As an application, starting from the Monge-Ampère setting introduced in [3], we get a space of homogeneous type modeling the real analysis for such an equation.

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References

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Authors
  1. H. Aimar
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  2. L. Forzani
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  3. R. Toledano
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Additional information

Acknowledgements and Notes. Supported by Programa Especial de Matemática Aplicada (CONICET) and Prog. CAI+D, UNL.

Programa Especial de Matemática Aplicada (CONICET), Dpto. de Matemática, FIQ. UNL.

Programa Especial de Matemática Aplicada (CONICET), Dpto. de Matemática, FIQ. UNL.

Programa Especial de Matemática-Aplicada (CONICET), Dpto. de Matemática, FCEF-QyN, UNRC.

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Aimar, H., Forzani, L. & Toledano, R. Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampère equation. The Journal of Fourier Analysis and Applications 4, 377–381 (1998). https://doi.org/10.1007/BF02498215

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  • DOI: https://doi.org/10.1007/BF02498215

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