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The Logic of a Classical System
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a-algebra a-finite measure abelian analytic assume automorphism bilinear form Boolean algebra Boolean subalgebra Borel function Borel group Borel map Borel measure Borel set Borel space Borel structure central extension Chapter classical closed linear manifold cocycle commutes complex numbers containing continuous corollary corresponding countable defined denote division ring elements equation equivalence classes exists a Borel finite dimensional follows frame function g e G G-space geometry Haar measure hence Hilbert space homomorphism identity implies induced irreducible representation isomorphism lattice lcsc group lemma Let G Lie algebra Lie group logic multiplier Neumann nonnegative obtain obvious one-one open set orthogonal particle physical projection valued measure prove Quantum Mechanics real number representation of G satisfied self-adjoint operator semisimple sequence shows simply connected standard Borel strict cocycle subspace Suppose system of imprimitivity theorem theory topology transformations trivial vector space write