Theorems · Theorem · measure theory

MeasureTheory.setIntegral_mono_set

∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : PartialOrder E] [IsOrderedAddMonoid E] [IsOrderedModule ℝ E] {μ : MeasureTheory.Measure X} {f : X → E}
  {s t : Set X} [OrderClosedTopology E],
  MeasureTheory.IntegrableOn f t μ → 0 ≤ᵐ[μ.restrict t] f → s ≤ᵐ[μ] t → ∫ (x : X) in s, f x ∂μ ≤ ∫ (x : X) in t, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

10 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpacePartialOrderIsOrderedAddMonoidIsOrderedModuleOrderClosedTopology