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- Title
MONOTONICITY PROPERTIES OF DARBOUX SUMS.
- Authors
Kyrezi, Ioanna
- Abstract
Let ƒ : [a; b] → ℝ be a continuous function. Dividing the interval [a; b] into subintervals of equal length, we obtain partitions of [a; b] for which the upper and lower Darboux sums of ƒ constitute two sequences, which converge to the definite integral of ƒ in [a; b] from above and below respectively. We study the monotonicity properties of these sequence and we prove that their non-monotonicity is a generic quasisure) property in the space C([a; b]).
- Subjects
CONTINUOUS functions; DARBOUX transformations; MATHEMATICAL transformations; PARTITIONS (Mathematics); MATHEMATICAL sequences
- Publication
Real Analysis Exchange, 2010, Vol 35, Issue 1, p43
- ISSN
0147-1937
- Publication type
Article
- DOI
10.14321/realanalexch.35.1.0043