Theorems · Theorem · measure theory

LinearIsometryEquiv.integrable_comp_iff

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_8} {H : Type u_9}
  [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup H] {𝕜 : Type u_10} {𝕜' : Type u_11}
  [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NontriviallyNormedField 𝕜'] [inst_4 : NormedSpace 𝕜' E]
  [inst_5 : NormedSpace 𝕜 H] {σ : 𝕜 →+* 𝕜'} {σ' : 𝕜' →+* 𝕜} [RingHomIsometric σ] [RingHomIsometric σ']
  [inst_8 : RingHomInvPair σ σ'] [inst_9 : RingHomInvPair σ' σ] {φ : α → H} (L : H ≃ₛₗᵢ[σ] E),
  MeasureTheory.Integrable (fun a => L (φ a)) μ ↔ MeasureTheory.Integrable φ μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

2 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNontriviallyNormedFieldNontriviallyNormedFieldNormedSpaceNormedSpaceRingHomIsometricRingHomIsometricRingHomInvPairRingHomInvPair