OAI/Analysis/ModularTheory/LpFaithful.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

Faithfulness of the concrete modular representation for Lebesgue measure. The fixed interval [0,1] gives an isometric copy of the original Hilbert space and detects every constant operator before gauge conjugation.

  1. def OAI.WeakPureInfiniteness.lpIntervalVector line 18
  2. lemma OAI.WeakPureInfiniteness.lpIntervalVector_norm line 22
  3. lemma OAI.WeakPureInfiniteness.lpIntervalVector_sub line 27
  4. lemma OAI.WeakPureInfiniteness.lpIntervalVector_injective line 32
  5. lemma OAI.WeakPureInfiniteness.pointwiseLpRepresentation_interval line 38
  6. theorem OAI.WeakPureInfiniteness.pointwiseLpRepresentation_injective line 55
  7. theorem OAI.WeakPureInfiniteness.modularLpRepresentation_injective line 63