Theorems · Theorem · measure theory

MeasureTheory.L1.norm_setToL1_le_mul_norm

∀ {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}
  [inst_4 : CompleteSpace F] {T : Set α → E →L[ℝ] F} {C : ℝ} (hT : MeasureTheory.DominatedFinMeasAdditive μ T C),
  0 ≤ C → ∀ (f : ↥(MeasureTheory.Lp E 1 μ)), ‖(MeasureTheory.L1.setToL1 hT) f‖ ≤ C * ‖f‖

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

3 results in Mathlib

Foundations

Depth 241 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace