= Translation continuity in Lp on a locally compact group
{title2=$\|T_xf-f\|_p\longrightarrow0\quad(x\longrightarrow e)$}
For left <Haar measure>, $T_xf(t)=f(x^{-1}t)$ is an isometry on $L^p(G)$, $1\leq p<\infty$. For compactly supported continuous functions, uniform continuity on a slightly enlarged compact support proves norm continuity. Approximation by those functions and the triangle inequality extend it to all $L^p$. The continuous image of a compact set of translation parameters is consequently compact in $L^p$.
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