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(Satellite conference of the World Congress ICM2006, Madrid 2006)This paper is a survey of the results of Bombal and I. Villanueva Díez [Funct. Approx. Comment. Math. 26 (1998), 117–126; Bombal, D. Pérez-García and Villanueva Díez [Q. J. Math. 55 (2004), no. 4, 441–450; and Pérez-García and Villanueva Díez [Ark. Mat. 42 (2004), no. 1, 153–171; The results surveyed concern Riesz-type integral representations of continuous multilinear operators on C(K) -spaces by polymeasures.engjournal articlehttp://www.eweb.unex.es/eweb/extracta/Vol-22-2/22P2Bomba-congreso.pdfhttp://www.eweb.unex.es/eweb/extracta/restricted access517.983.2multilinear operatorspolymeasuresAnálisis funcional y teoría de operadores