Why is the LIBOR-market model free of arbitrage?

Recently I have been reading a lot on the market models.

One thing that keeps escaping me - why is the Libor-market model (LMM) assumed to e free of aritrage in continuous time ?

To me this means that there must be a Numeraire so that all the bond-price-processes $P(t,T^*)$ with $T^* >t$ and $T^* \in [0,T]$ (with $T>T^*$ ) are martingales und the measure associated with that numeraire.

To state that the LMM is free of aritrage someone must have determines the relevant numeraire and done all the necessary checks. Is there a book or paper where those resuls can be found?

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