On functions of bounded variation relative to a set

Autor:	P. C. Bhakta
Rok vydání:	1972
Předmět:	Pure mathematics Bounded set Bounded function Bounded variation ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Uniform boundedness Bounded deformation Caccioppoli set Bounded mean oscillation Bounded operator Mathematics
Zdroj:	Journal of the Australian Mathematical Society. 13:313-322
ISSN:	0004-9735 1446-7887
DOI:	10.1017/s1446788700013720
Popis:	The present paper on functions of bounded variation relative to a set has its point of departure in the work of R. L. Jeffery [10]. Below we recapitulate Jeffery's class U of functions of bounded variation relative to a set, we state and prove a number of preliminary lemmas and theorems, we introduce a suitable pseudo- metric space (X, d) of such functions, and the analogous space , and prove that (X, d) is separable, that every closed sphere in (X, d) is compact and that is complete. These results extend known results of C. R. Adams, and C. R. Adams and A. P. Morse for the space of usual BV functions.
Databáze:	OpenAIRE
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