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MEASURE THEORY ON GSPACES 1 Borel spaces and Borel maps
Locally compact groups Haar measure
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a-finite measure abelian analytic associated automorphism Borel function Borel group Borel map Borel measure Borel set Borel structure central extension Chapter cocycle commutes compact set complex numbers continuous coordinate system Corollary corresponding countable covering group defined denote elements equation equivalence class ergodic exists a Borel follows formula g e G G-space group G Haar measure Hence Hilbert space identity implies induced invariant measure class irreducible representation lcsc group left invariant lemma Let G Lie algebra Lie group linear Lorentz group map of G matrices multiplier for G observables obtain one-one open set orbit projection valued measure projective representation Proof prove quantum mechanical quasi-invariant measure representation of G satisfied self-adjoint semidirect product semisimple shows simply connected stability group stability subgroup standard Borel space strict cocycle subspace Suppose system of imprimitivity theorem theory topology transformation transitive trivial unitary operator vector space write