Theorems · Definition · measure theory

MeasureTheory.L1.setToL1

{α : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : NormedAddCommGroup E] →
        [inst_1 : NormedSpace ℝ E] →
          [inst_2 : NormedAddCommGroup F] →
            [inst_3 : NormedSpace ℝ F] →
              {m : MeasurableSpace α} →
                {μ : MeasureTheory.Measure α} →
                  [CompleteSpace F] →
                    {T : Set α → E →L[ℝ] F} →
                      {C : ℝ} → MeasureTheory.DominatedFinMeasAdditive μ T C → ↥(MeasureTheory.Lp E 1 μ) →L[ℝ] F

Extend Set α → E →L[ℝ] F to (α →₁[μ] E) →L[ℝ] F.

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

44 results in Mathlib

Foundations

Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace