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I have stumbled upon the notion of a $K$-valued Haar integral on a locally compact group, where $K$ is a non-Archimedean field, as well as the $K$-valued modular function, in an article of Schikhof. He cites his thesis "Non-archimedean harmonic analysis", but I have not been able to find that book anywhere. Is there any other more accessible reference where I could read about this? I am particularly interested in the $p$-adic case.

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You will find it in the following link:

https://repository.ubn.ru.nl/bitstream/handle/2066/107512/mmubn000001_234785616.pdf?sequence=1

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