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Theorems · Theorem · measure theory

MeasureTheory.Measure.isOpenPosMeasure_smul

∀ {X : Type u_1} [inst : TopologicalSpace X] {m : MeasurableSpace X} (μ : MeasureTheory.Measure X) [μ.IsOpenPosMeasure]
  {c : ENNReal}, c ≠ 0 → (c • μ).IsOpenPosMeasure
Defined in
Mathlib.MeasureTheory.Measure.OpenPos
Cited by
2 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceMeasureTheory.Measure.IsOpenPosMeasure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.IsHaarMeasure.smul · cited by 2IsHaarMeasure.smulMeasureTheory.Measure.IsAddHaarMeasure.smul · cited by 2IsAddHaarMeasure.smulSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.Nonempty · cited by 2627Set.NonemptyIsOpen · cited by 2400IsOpenmul_ne_zero · cited by 178mul_ne_zeroMeasureTheory.Measure.IsOpenPosMeasure · cited by 80Measure.IsOpenPosMeasureIsOpen.measure_ne_zero · cited by 6IsOpen.measure_ne_zeroMeasure.isOpenPosMeasure_smulCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.