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We present the notion of monotone solution of mean field games masterequations in the case of a continuous state space. We establish the existence,uniqueness and stability of such solutions under standard assumptions. Thisnotion allows us to work with solutions which are merely continuous in themeasure argument, in the case of first order master equations. We study severalstructures of common noises, in particular ones in which common jumps (oraggregate shocks) can happen randomly, and ones in which the correlation ofrandomness is carried by an additional parameter.

Monotone solutions for mean field games master equations : continuous state space and common noise