Theorems · Theorem · measure theory

MeasureTheory.Measure.measure_Ioo_pos

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : LinearOrder X] [OrderTopology X] {m : MeasurableSpace X}
  (μ : MeasureTheory.Measure X) [μ.IsOpenPosMeasure] [DenselyOrdered X] {a b : X}, 0 < μ (Set.Ioo a b) ↔ a < b

Defined in

Mathlib.MeasureTheory.Measure.OpenPos

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyMeasureTheory.Measure.IsOpenPosMeasureDenselyOrdered