Theorems · Theorem · measure theory

MeasureTheory.integral_mono_of_nonneg

∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} [inst_2 : PartialOrder E] [IsOrderedAddMonoid E] [IsOrderedModule ℝ E]
  [ClosedIciTopology E] {f g : α → E},
  0 ≤ᵐ[μ] f → MeasureTheory.Integrable g μ → f ≤ᵐ[μ] g → ∫ (a : α), f a ∂μ ≤ ∫ (a : α), g a ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

16 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpacePartialOrderIsOrderedAddMonoidIsOrderedModuleClosedIciTopology