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That's the definition of exact form in $E$. But if we look at the definition 10.18 we see that $\lambda \in C'$ but Rudin skip this condition.

Can anyone please explain this moment

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    $\begingroup$ It would have been better to be explicit about the differentiability assumptions, I think, but Rudin left them implicit here. He's talking about $d\lambda$, so $\lambda$ has to be a form for which $d\lambda$ makes sense. I don't think Rudin has extended the notion to more general forms in the book, so $\lambda$ would need to be continuously differentiable. $\endgroup$ – Daniel Fischer May 9 '16 at 18:13
  • $\begingroup$ @DanielFischer, Hello! Can you help please with this? I am dealing with this couple days and no ideas. math.stackexchange.com/questions/1779261/… $\endgroup$ – ZFR May 10 '16 at 9:20
  • $\begingroup$ @DanielFischer, I would so grateful for your help, Daniel! $\endgroup$ – ZFR May 10 '16 at 9:28

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