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Theorems · Definition · measure theory

MeasureTheory.Content.outerMeasure

{G : Type w} → [inst : TopologicalSpace G] → MeasureTheory.Content G → MeasureTheory.OuterMeasure G

Extending a content on compact sets to an outer measure on all sets.

Defined in
Mathlib.MeasureTheory.Measure.Content
Cited by
24 results in Mathlib
Foundations
Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

MeasureTheory.Content.measure · cited by 10Content.measureMeasureTheory.Content.measure_apply · cited by 6Content.measure_applyMeasureTheory.Content.outerMeasure_opens · cited by 6Content.outerMeasure_opensMeasureTheory.Content.le_outerMeasure_compacts · cited by 2Content.le_outerMeasure_c…MeasureTheory.Content.outerMeasure_eq_iInf · cited by 2Content.outerMeasure_eq_i…MeasureTheory.Content.outerMeasure_lt_top_of_isCompact · cited by 2Content.outerMeasure_lt_t…MeasureTheory.Content.outerMeasure_preimage · cited by 2Content.outerMeasure_prei…MeasureTheory.Measure.haar.haarContent_outerMeasure_closure_pos · cited by 1haar.haarContent_outerMea…MeasureTheory.Measure.haar.haarContent_outerMeasure_self_pos · cited by 1haar.haarContent_outerMea…MeasureTheory.Content.borel_le_caratheodory · cited by 1Content.borel_le_caratheo…MeasureTheory.Measure.haar.addHaarContent_outerMeasure_closure_pos · cited by 1haar.addHaarContent_outer…MeasureTheory.Measure.haar.addHaarContent_outerMeasure_self_pos · cited by 1haar.addHaarContent_outer…MeasureTheory.Content.outerMeasure_caratheodory · cited by 1Content.outerMeasure_cara…MeasureTheory.Content.outerMeasure_exists_open · cited by 1Content.outerMeasure_exis…MeasureTheory.Content.outerMeasure_interior_compacts · cited by 1Content.outerMeasure_inte…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsOpen · cited by 2400IsOpenMeasureTheory.OuterMeasure · cited by 287MeasureTheory.OuterMeasureMeasureTheory.Content · cited by 60MeasureTheory.ContentisOpen_empty · cited by 23isOpen_emptyMeasureTheory.Content.innerContent · cited by 22Content.innerContentMeasureTheory.inducedOuterMeasure · cited by 22MeasureTheory.inducedOute…MeasureTheory.Content.innerContent_bot · cited by 3Content.innerContent_botContent.outerMeasureCITED BYCITES

Cites9

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

Cited by25

Results whose statement or proof uses this declaration.