Lie Groups of Measurable Mappings

We describe new construction principles for infinite-dimensional Lie groups. In particular, given any measure space (X,(Sigma),(mu)) and (possibly infinite-dimensional) Lie group G, we construct a Lie group L^(infnity) (X,G), which is a Frechet-Lie group if G is so. We also show that the weak direct product (n-ary product)^*i(element of) I Gi of an arbitrary family (Gi)i(element of) I of Lie groups can be made a Lie group, modelled on the locally convex direct sum (ciculed plus)i(element of) I L(Gi).