Theorems · Definition · functional analysis

ContinuousLinearMap.compLp

{α : Type u_1} →
  {E : Type u_4} →
    {F : Type u_5} →
      {m : MeasurableSpace α} →
        {p : ENNReal} →
          {μ : MeasureTheory.Measure α} →
            [inst : NormedAddCommGroup E] →
              [inst_1 : NormedAddCommGroup F] →
                {𝕜 : Type u_6} →
                  {𝕜' : Type u_7} →
                    [inst_2 : NontriviallyNormedField 𝕜] →
                      [inst_3 : NontriviallyNormedField 𝕜'] →
                        [inst_4 : NormedSpace 𝕜 E] →
                          [inst_5 : NormedSpace 𝕜' F] →
                            {σ : 𝕜 →+* 𝕜'} →
                              [RingHomIsometric σ] →
                                (E →SL[σ] F) → ↥(MeasureTheory.Lp E p μ) → ↥(MeasureTheory.Lp F p μ)

Composing f : Lp with L : E →L[𝕜] F.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

17 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNontriviallyNormedFieldNontriviallyNormedFieldNormedSpaceNormedSpaceRingHomIsometric