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Theorems · Theorem · functional analysis

lp.norm_eq_ciSup

∀ {α : Type u_3} {E : α → Type u_4} [inst : (i : α) → NormedAddCommGroup (E i)] (f : ↥(lp E ⊤)), ‖f‖ = ⨆ i, ‖↑f i‖
Defined in
Mathlib.Analysis.Normed.Lp.lpSpace
Cited by
3 results in Mathlib
Foundations
Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

lp.isLUB_norm · cited by 6lp.isLUB_normlp.norm_nonneg' · cited by 6lp.norm_nonneg'equiv_lpPiLp_norm · cited by 0equiv_lpPiLp_normReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topNorm.norm · cited by 5413Norm.normAddSubgroup · cited by 3232AddSubgroupiSup · cited by 2415iSupPreLp · cited by 163PreLplp · cited by 157lplp.norm_eq_ciSupCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Realstatement · cited by 25,697
  • NormedAddCommGroupstatement and proof · cited by 15,752
  • ENNRealstatement · cited by 9,879
  • Top.topstatement and proof · cited by 9,680
  • Norm.normstatement · cited by 5,413
  • AddSubgroupstatement · cited by 3,232
  • iSupstatement · cited by 2,415
  • PreLpstatement and proof · cited by 163
  • lpstatement and proof · cited by 157

Cited by3

Results whose statement or proof uses this declaration.