Theorems · Definition · measure theory

MeasureTheory.setToFun

{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) →
                  (T : Set α → E →L[ℝ] F) → {C : ℝ} → MeasureTheory.DominatedFinMeasAdditive μ T C → (α → E) → F

Extend T : Set α → E →L[ℝ] F to (α → E) → F (for integrable functions α → E). We set it to 0 if the function is not integrable or if the target space is not complete.

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

77 results in Mathlib

Foundations

Depth 240 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace