In [this paper](https://www.researchgate.net/publication/254211850_Non-archimedean_function_spaces_and_the_Lebesgue_dominated_convergence_theorem), the authors explain that the full generality of the Lebesgue dominated convergence theorem holds for functions on a compact zero-dimensional space $X$ taking values in a metrically complete non-archimedean field $K$ if and only if $X$ is finite. However, they remark that "On the other hand, in [11, Theorem 4.13] Katsaras showed a Lebesgue dominated convergence theorem for a certain class of measures $μ$ on $X$"


The paper in question is:


A.K. Katsaras, *On $p$-adic vector measure spaces*, J. Math. Anal. Appl., 365 (2010)


Unfortunately, this paper does not seem to be available. Also, be warned, there is a paper by the same author published in 2009 with a nearly identical title which *is* available, but which does not contain what I need.


I would very much like to know what the details are about this version of Katsaras' Lebesgue Dominated Convergence Theorem.


More generally, being a late-stage PhD student whose research has taken him into this subject, and who has no one to talk to —none of the mathematicians at my university know the slightest bit about non-Archimedean (functional) analysis— a book or paper dealing with convergence theorems and the like for non-Archimedean valued integrals/measures would be much appreciated. Ideally, I'd like an expert to talk to; most of the literature takes such a general approach to the subject that I can barely make heads or tails of what I'm reading.



Non-Archimedean Lebesgue dominated convergence theorem
Here's the correct DOI link for the paper referenced: <https://doi.org/10.1016/j.jmaa.2009.10.059>


Paper is in Open Archive so I am pretty sure you can view it yourself.


AFAICT, the reference is correct (Theorem 4.13 in the above-linked paper is a Dominated Convergence Theorem). Here is the full bibliographic reference:



> 
> Journal of Mathematical Analysis and Applications
> Volume 365, Issue 1, 1 May 2010, Pages 342-357
> 
> 
> 


