Geodesic
Generalized capacities, compound curves and removable sets
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 100-119
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Relations between the generalized capacity of a condenser in sense of Aikawa–Ohtsuka and the module of a family of compound curves connecting the condenser plates through a given set are established. Conditions of the removability of compact for the generalized capacity of a condenser are obtained. Properties of the extremal length of vector measures are used. 
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Yu. V. Dymchenko; V. A. Shlyk. Generalized capacities, compound curves and removable sets. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 100-119. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a5/

[1] K. Kuratovskii, Topologiya, v. 2, M., 1969

[2] P. A. Pugach, V. A. Shlyk, “Obobschennye emkosti i poliedralnye poverkhnosti”, Zap. nauchn. semin. POMI, 383, 2010, 148–178 | MR

[3] P. A. Pugach, V. A. Shlyk, “Ustranimye mnozhestva dlya obobschennogo modulya semeistva poverkhnostei”, Zap. nauchn. semin. POMI, 392, 2011, 163–190 | MR

[4] V. A. Shlyk, “Normalnye oblasti i ustranimye osobennosti”, Izv. RAN, ser. mat., 57:4 (1993), 92–117 | MR | Zbl

[5] H. Aikawa, M. Ohtsuka, “Extremal length of vector measures”, Ann. Acad. Sci. Fenn. Math., 24 (1999), 61–88 | MR | Zbl

[6] B. Fuglede, “Extremal length and functional completion”, Acta Math., 126 (1957), 171–219 | DOI | MR

[7] L. I. Hedberg, “Removable singularities and condenser capacities”, Ark. Mat., 12 (1974), 181–201 | DOI | MR | Zbl

[8] B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal functions”, Trans. Amer. Math. Soc., 192 (1972), 207–226 | DOI | MR

[9] M. Ohtsuka, Extremal length and precise functions, GAKUTO International Series, Mathematical Sciences and Applications, 19, Gakkōtosho Co., Ltd, Tokyo, 2003 | MR | Zbl