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## Main Question or Discussion Point

What restrictions must we place on a real-valued function [tex]F[/tex] for

[tex]

F(x) = \frac{d}{dx} \int_a^x F'(y)dy

[/tex]

to hold, where "[itex]\int[/itex]" is the Lebesgue integral?

[tex]

F(x) = \frac{d}{dx} \int_a^x F'(y)dy

[/tex]

to hold, where "[itex]\int[/itex]" is the Lebesgue integral?