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A Constructive Look at Functions of Bounded Variation
Author(s) -
Bridges Douglas S.
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609399006736
Subject(s) - bounded variation , mathematics , variation (astronomy) , constructive , bounded function , interval (graph theory) , property (philosophy) , function (biology) , continuous function (set theory) , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , process (computing) , computer science , physics , astrophysics , operating system , philosophy , epistemology , evolutionary biology , biology
Functions with bounded variation and with a (total) variation are examined within Bishop's constructive mathematics. It is shown that the property of having a variation is hereditary downward on compact intervals, and hence that a real‐valued function f with a variation on a compact interval can be expressed as a difference of two increasing functions. Moreover, if f is sequentially continuous, then the corresponding variation function, and hence f itself, is uniformly continuous. 1991 Mathematics Subject Classification 26A45.