If G is a locally compact group and K subse G is compact, and

lim n --> inf int_K f_n(x) dx = 0, then does lim n --> inf int_{K^-1} f_n(x^-1) dx = 0? (f_n subset L^p(G) for some p >= 1) I actually ultimately need this question asked for integration being Bochner integration, but is this true even for Lebesgue integrals? I don't think it is, since the modular function will screw things up even if it's a 'mild' function.

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