Theorems · Theorem · functional analysis

ContinuousLinearMap.holder.congr_simp

∀ {α : Type u_1} {𝕜 : Type u_2} {E : Type u_3} {F : Type u_4} {G : Type u_5} {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {p q : ENNReal} (r : ENNReal) [hpqr : p.HolderTriple q r]
  [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedAddCommGroup F]
  [inst_3 : NormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜 F] [inst_6 : NormedSpace 𝕜 G]
  (B B_1 : E →L[𝕜] F →L[𝕜] G),
  B = B_1 →
    ∀ (f f_1 : ↥(MeasureTheory.Lp E p μ)),
      f = f_1 →
        ∀ (g g_1 : ↥(MeasureTheory.Lp F q μ)),
          g = g_1 → ContinuousLinearMap.holder r B f g = ContinuousLinearMap.holder r B_1 f_1 g_1

Defined in

Mathlib.MeasureTheory.Function.Holder

Cited by

0 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENNReal.HolderTripleNontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpace