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We prove the existence of a weak solution to the following Dirichlet problem $$ \left\{ \begin{aligned} &\mathcal A u-\mathfrak{B}u + \Phi(x,u,\nabla u)=f\quad \mbox{in } \Omega,\\ & u\in W_0^{1,\overrightarrow{p}}(Omega), \quad \Phi(x,u…

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We consider omega-regular winning conditions on the resulting infinite state sequence. To model the independent choice of moves, both players are allowed to use randomization for selecting their moves.

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