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In this paper we calculate the next-to-leading order (NLO) QCD $[{\cal O}(\alpha_s \alpha^3)]$ and electroweak (EW) $[{\cal O}(\alpha^4)]$ corrections to the $WWW$ production at the LHC and deal with the subsequent leptonic decays from $W$ bosons by adopting an improved narrow-width approximation which takes into account the spin correlation and finite-width effects.
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