Theorems · Theorem · measure theory

MeasureTheory.ae_const_le_iff_forall_lt_measure_zero

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_2} [inst : LinearOrder β]
  [inst_1 : TopologicalSpace β] [OrderTopology β] [FirstCountableTopology β] (f : α → β) (c : β),
  (∀ᵐ (x : α) ∂μ, c ≤ f x) ↔ ∀ b < c, μ {x | f x ≤ b} = 0

Defined in

Mathlib.MeasureTheory.Function.AEEqOfLIntegral

Cited by

3 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceOrderTopologyFirstCountableTopology