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On considere le probleme de Cauchy u(x,o)=0, ∂u(x,o)/∂t=f(x) pour une equation d'ordre 2 fortement hyperbolique a n dimensions d'espace n≥3 et coefficients C ∞ . On demontre la convergence presque partout de la solution pour les donnees initiales pour f dans L p

On a.e. convergence of solutions of hyperbolic equations to 𝐿^{𝑝}-initial data