Semi-invariant integration with values in a group and some of its applications

Every continuous mapping of a connected compact group into a locally compact abelian group decomposes into the sum of a contractible mapping and a homomorphism. There is constructed an integral which is invariant on the first summand and which annihilates the second. The construction is applied to describe certain continuous cohomologies of groups and to classify automorphisms.
Bibliography: 15 titles.