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A Characterization of the Lebesgue Integral

Published online by Cambridge University Press:  20 November 2018

B. S. Thomson
B. S. Thomson*
Affiliation:
Dept. of Maths, Simon Fraser University, Burnaby, B.C. , CanadaV5A 1S6
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The first general integrability criterion is due to Riemann. He observed that a necessary and sufficient condition for a function f(x) on [a, b] to be integrable in his sense is that for each ε > 0 there exists a δ > 0 so that

where {x0, x1, …, xn} is a partition of [a, b] with diameter less than δ (and ω(f, I) denotes the oscillation of f on the interval I).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 3 , 01 September 1977 , pp. 353 - 357
Copyright
Copyright © Canadian Mathematical Society 1977

References

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