Geodesic
Metric Rademacher Theorem and the Area Formula for Metric-Valued Lipschitz Mappings
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 4, pp. 50-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a new proof of the metric analog of Rademacher Theorem and the area formula for metric-valued mappings. 
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M. B. Karmanova. Metric Rademacher Theorem and the Area Formula for Metric-Valued Lipschitz Mappings. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 4, pp. 50-69. http://geodesic.mathdoc.fr/item/VNGU_2006_6_4_a2/

[1] Federer H., Geometric measure theory, Springer, N.Y., 1969 | MR | Zbl

[2] Karmanova M. B., “Formuly ploschadi i koploschadi dlya otobrazhenii klassov Soboleva so znacheniyami v metricheskom prostranstve”, Sib. mat. zhurn., 2007 (to appear)

[3] Kirchheim B., “Rectifiable metric spaces: local structure and regularity of the Hausdorff measure”, Proc. AMS, 121 (1994), 113–123 | DOI | MR | Zbl

[4] Reshetnyak Yu. G., “Sobolevskie klassy funktsii so znacheniyami v metricheskom prostranstve”, Sib. mat. zhurn., 38:3 (1997), 657–675

[5] Stein E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970 | MR

[6] Vodopyanov S. K., “$\mathcal{P}$-differentiability on Carnot groups in different topologies and related topics”, Tr. po analizu i geometrii, Izd-vo In-ta matematiki, Novosibirsk, 2000, 603–670 | MR | Zbl

[7] Vodopyanov S. K., Teoriya integrala Lebega, Zapiski lektsii po matematicheskomu analizu, Izd-vo NGU, Novosibirsk, 2003

[8] Vodopyanov S. K., “Geometriya prostranstv Karno–Karateodori, kvazikonformnyi analiz i geometricheskaya teoriya mery”, Mat. zhurn. Vladikavkaz, 5:1 (2003), 1–14

[9] Karmanova M. B., “Metricheskaya differentsiruemost otobrazhenii i geometricheskaya teoriya mery”, Dokl. AN, 401:4 (2005), 443–447 | MR | Zbl

[10] Karmanova M. B., “Spryamlyaemye mnozhestva i formula koploschadi dlya otobrazhenii so znacheniyami v metricheskom prostranstve”, Dokl. AN, 408:1 (2006), 16–21 | MR

[11] Maria Karmanova, “Geometric Measure Theory Formulas on Rectifiable Metric Spaces, Analysis and Geometry in Their Interaction”, Contemporary Mathematics, AMS, 2007 (to appear) | MR