Cohomology in Ergodic theory

In ergodic theory, cohomological questions appear at many places. For example in the construction of some Schroedinger operators (PDF file) with a theorem of Feldman and Moore (PDF file) .
coboundary Maybe the simplest cohomology group is defined for an automorphism T: X -> X of a Lebesgue space (X,A,m). The group of measurable sets A (with symmetric difference + as groupoperation) modulo the subgroup { Z = Y + T(Y) } of all coboundaries is the first cohomology group of the Z action with structure group Z 2 .

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