Abstract
Introduction. The characterization of the Lebesgue area as a functional 4) defined on a certain class of continuous mappings has attracted a great deal of attention. The conditions that are imposed upon a functional -I in this paper (see Section 3) are essentially those listed in L. Cesari [2; 7. 5]. Let Z be the class of all continuous mappings (T,A) from an admissible subset A of E2 into E, (see SectioIn 1), anld let L(T,A) be the Lebesgue area of (T; A). A subclass Z' of Z is considered which consists of all miappings (T, A) in Z admitting aii elementary shirinking approach (see Sectioni 4), and it is shown that Z' is the class of mappings on which each functional @ satisfying the conditions of Section 3 agrees with the Lebesgue area.
Published Version
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