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Theorems · Definition · functional analysis

PiLp.uniformEquiv

(p : ENNReal) →
  {ι : Type u_2} → (β : ι → Type u_4) → [inst : (i : ι) → UniformSpace (β i)] → PiLp p β ≃ᵤ ((i : ι) → β i)

WithLp.equiv as a uniform isomorphism.

Defined in
Mathlib.Analysis.Normed.Lp.PiLp
Cited by
2 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

PiLp.toEquiv_uniformEquiv · cited by 0PiLp.toEquiv_uniformEquivPiLp.toHomeomorph_uniformEquiv · cited by 0PiLp.toHomeomorph_uniform…ENNReal · cited by 9879ENNRealEquiv · cited by 8337EquivUniformSpace · cited by 2040UniformSpacePiLp · cited by 150PiLpUniformEquiv · cited by 80UniformEquivWithLp.equiv · cited by 8WithLp.equivPiLp.uniformContinuous_ofLp · cited by 0PiLp.uniformContinuous_of…PiLp.uniformContinuous_toLp · cited by 0PiLp.uniformContinuous_to…PiLp.uniformEquivCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.