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- W4246290189 abstract "Using the generalized Riemann approach to Lebesgue integration we define a new property which is equivalent to Lebesgue integrability for measurable functions. Roughly speaking, this property says that Riemann sums for sufficiently fine partitions of sufficiently small intervals can always be made arbitrarily small. We formulate this property in such a way that it applies to either Lebesgue integration or Perron integration, thus correcting a defect in earlier versions of this idea. The condition of measurability is used only in preliminary results to insure that the support of functions can always be assumed to be ${G_delta }$-sets." @default.
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- W4246290189 date "1986-01-01" @default.
- W4246290189 modified "2023-09-28" @default.
- W4246290189 title "A New Property Equivalent to Lebesgue Integrability" @default.
- W4246290189 doi "https://doi.org/10.2307/2045662" @default.
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