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- W2028509232 abstract "Let F map [0, 1] into a Banach space B and let R(F) denote the set of all limits of Riemann sums of F . The set R(F) need not be convex in general (Nakamura and Amemiya (1966)) but is always convex when B is finite dimensional as first shown by Hartman (1947). A proof of Hartman's result, based on a description of R(F) when the range of F is finite, was given in Ellis (1959). In this note this description is refined, the extreme points of R ( F ) are determined and the following complete characterization of R ( F ) is obtained (where N n = {1,2, …, n})." @default.
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- W2028509232 date "1975-08-01" @default.
- W2028509232 modified "2023-10-18" @default.
- W2028509232 title "On the set of limits of Riemann sums" @default.
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- W2028509232 doi "https://doi.org/10.1017/s1446788700023934" @default.
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