Geodesic
Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 3, pp. 381-396

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Nondegenerate $\sigma$-additive measures with ranges in $\mathbb R$ and $\mathbb Q_q$ ($q\ne p$ are prime numbers) that are quasi-invariant and pseudodifferentiable with respect to dense subgroups $G'$ are constructed on diffeomorphism and homeomorphism groups $G$ for separable non-Archimedean Banach manifolds $M$ over a local field $\mathbb K$, $\mathbb K\supset\mathbb Q_p$, where $\mathbb Q_p$ is the field of $p$-adic numbers. These measures and the associated irreducible representations are used in the non-Archimedean gravitation theory. 
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     author = {S. V. Lyudkovskii},
     title = {Measures on diffeomorphism groups for {non-Archimedean} manifolds: {Group} representations and their applications},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {381--396},
     publisher = {mathdoc},
     volume = {119},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_119_3_a2/}
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S. V. Lyudkovskii. Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications. Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 3, pp. 381-396. http://geodesic.mathdoc.fr/item/TMF_1999_119_3_a2/