Does anyone know, where I can find the proof of necessary and sufficient conditions for differentiating under the integral sign in case of Henstock integral? Here are the theorems but not all the proofs:



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> *Necessary and sufficient conditions for differentiating under the integral sign*  
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>  Erik Talvila  
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> [arXiv:math/0101012](http://arxiv.org/abs/math/0101012)
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> We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every derivative. The Henstock integral is thus used in an essential way.   
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Henstock, Differentiation under the integral sign
Bartle's *A modern theory of integration* has it on [pp. 199-200](https://books.google.com/books?id=6-9royzoBL8C&pg=PA199).


