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- W2022296887 abstract "Benedetto Bongiorno constructed a certain class of improperly Riemann integrable functions on [ 0 , 1 ] which are not first-return integrable. He asked if all improper Riemann integrable functions which are not Lebesgue integrable are not first-return integrable. Recently David Fremlin provided a clever example to show that this is not the case. It remains open as to which functions are first-return integrable. We prove two general theorems which imply the existence of a large class of improperly Riemann integrable functions which are not first-return integrable. As a corollary we obtain that there is an improperly Riemann integrable function which is C ∞ on ( 0 , 1 ] yet fails to be first-return integrable." @default.
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- W2022296887 date "2008-11-01" @default.
- W2022296887 modified "2023-10-18" @default.
- W2022296887 title "Functions not first-return integrable" @default.
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- W2022296887 doi "https://doi.org/10.1016/j.jmaa.2008.05.084" @default.
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