Theorems · Definition · measure theory

MeasureTheory.VectorMeasure.withDensity

{X : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      {G : Type u_4} →
        {mX : MeasurableSpace X} →
          [inst : NormedAddCommGroup E] →
            [inst_1 : NormedSpace ℝ E] →
              [inst_2 : NormedAddCommGroup F] →
                [inst_3 : NormedSpace ℝ F] →
                  [inst_4 : NormedAddCommGroup G] →
                    [inst_5 : NormedSpace ℝ G] →
                      MeasureTheory.VectorMeasure X F → (X → E) → (E →L[ℝ] F →L[ℝ] G) → MeasureTheory.VectorMeasure X G

The vector measure with density f with respect to a vector measure μ, associating to a measurable set the mass ∫ᵛ x in s, f x ∂[B; μ]. If f is not integrable, we use the junk value 0.

Defined in

Mathlib.MeasureTheory.VectorMeasure.WithDensityVec

Cited by

11 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace