Theorems · Theorem · measure theory

MeasureTheory.condExp_le_nonneg_const

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] [inst_3 : PartialOrder E] [ClosedIciTopology E] [IsOrderedAddMonoid E]
  [IsOrderedModule ℝ E] {f : α → E} {c : E}, 0 ≤ c → (∀ᵐ (x : α) ∂μ, f x ≤ c) → ∀ᵐ (x : α) ∂μ, μ[f | m] x ≤ c

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Real

Cited by

2 results in Mathlib

Foundations

Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpacePartialOrderClosedIciTopologyIsOrderedAddMonoidIsOrderedModule