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This article extends the celebrated sewing lemma to multi-parameter fields onhyper cubes. We use this to construct Young integrals for multi-parameterH\"older fields on general domains [0,1]^{k} with k>=1. Moreover, we showexistence, uniqueness and stability of some particular types of hyperbolicSPDE's driven by space-time H\"older noise in a Young regime  This article replaces the article "Rough Integration for Fields - withapplications to stochastic hyperbolic PDE's". Due to errors in the firstarticle in the section on rough fields, we have decided to divide this articleinto two parts. The first, is dealing with extending the sewing lemma togeneral multi parameter functions as well as hyperbolc equations driven bymultiparameter fields in a Young regime. The next article will come later andstudy the rough path type framework implied by the extended sewing lemma.

An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi parameter Young fields