Geodesic
Dense finitely generated subgroups and integration on compact groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 71-77.

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We point out methods of approximation of the commutator Hamiltonian on a compact group $G$ with finite sums of the form $\sum\limits_{g\in G}\sum\limits_{h\in G}\mu_g\nu_hghg^{-1}h^{-1}$, where $\sum\limits_{g\in G}\mu_g=1$ and $\sum\limits_{h\in G}\nu_h=1$. 
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     title = {Dense finitely generated subgroups and integration on compact groups},
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O. V. Gerasimova. Dense finitely generated subgroups and integration on compact groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 71-77. http://geodesic.mathdoc.fr/item/FPM_2013_18_4_a4/

[1] Gerasimova O. V., “Spektr kommutatornogo gamiltoniana vodorodopodoben”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2008, no. 6, 71–74 | MR

[2] Gerasimova O. V., “Spektr kommutatornogo gamiltoniana srodni energeticheskim urovnyam atoma vodoroda”, Uspekhi mat. nauk, 64:4 (2009), 177–178 | DOI | MR | Zbl

[3] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1984 | MR

[4] Winkelmann J., Dense random finitely generated subgroups of Lie groups, arXiv: math/0309129[math.GR]