Type: Article
Publication Date: 1977-09-01
Citations: 0
DOI: https://doi.org/10.4153/cmb-1977-053-3
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 { x 0 , x 1 , …, x n } is a partition of [a, b] with diameter less than δ (and ω( f, I ) denotes the oscillation of f on the interval I ).
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