Theorems · Theorem · measure theory

MeasureTheory.norm_setToFun_le_toReal

∀ {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} {f : α → E} (hT : MeasureTheory.DominatedFinMeasAdditive μ T C) (hC : 0 ≤ C),
  ‖MeasureTheory.setToFun μ T hT f‖ ≤ ↑(NNReal.mk C hC) * (∫⁻ (a : α), ENNReal.ofReal ‖f a‖ ∂μ).toReal

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

2 results in Mathlib

Foundations

Depth 243 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace