### Memory effects and $\text{\Gamma}$-convergence: A time dependent case.

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We give necessary and sufficient conditions which characterize the Young measures associated to two oscillating sequences of functions, on ${\omega}_{1}\times {\omega}_{2}$ and on ${\omega}_{2}$ satisfying the constraint ${v}_{n}\left(y\right)=\frac{1}{|{\omega}_{1}|}{\int}_{{\omega}_{1}}{u}_{n}(x,y)dx$. Our study is motivated by nonlinear effects induced by homogenization. Techniques based on equimeasurability and rearrangements are employed.

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