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Local Monomialization of Analytic Maps

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of characteristic zero proven in the author's earlier papers "Local monomialization of morphisms", Asterisque 260 (1999) and "Local monomialization of transcendental extensions", Annales de l'institut Fourier, 1517 - 1586.