I am having some doubts in the definitions of the upper and lower integrals in apostol.(adsbygoogle = window.adsbygoogle || []).push({});

There is a statement saying "Let S denote the set of all numbers [itex]_{a}[/itex][itex]\int[/itex] [itex]^{b}[/itex] s(x) dx obtained as s runs through all step functions below f i.e. S = { [itex]_{a}[/itex][itex]\int[/itex] [itex]^{b}[/itex] s(x) dx | s < f} "

I did not get this. Shouldn't S be a singleton with a only a single element being the summation of the area of all the step functions below f ?

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# Regarding Upper and lower integral sets.

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