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Theorems · Definition · measure theory

MeasureTheory.SimpleFunc.const

(α : Type u_5) → {β : Type u_6} → [inst : MeasurableSpace α] → β → MeasureTheory.SimpleFunc α β

Constant function as a SimpleFunc.

Defined in
Mathlib.MeasureTheory.Function.SimpleFunc
Cited by
50 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
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Around this declaration

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

MeasureTheory.lintegral_const · cited by 123MeasureTheory.lintegral_c…MeasureTheory.SimpleFunc.map · cited by 54SimpleFunc.mapMeasureTheory.stronglyMeasurable_const · cited by 47MeasureTheory.stronglyMea…MeasureTheory.lintegral_const_mul · cited by 19MeasureTheory.lintegral_c…MeasureTheory.lintegral_iSup · cited by 16MeasureTheory.lintegral_i…MeasureTheory.SimpleFunc.induction · cited by 14SimpleFunc.inductionMeasureTheory.Lp.simpleFunc.indicatorConst · cited by 14simpleFunc.indicatorConstMeasurableEmbedding.lintegral_map · cited by 10MeasurableEmbedding.linte…MeasureTheory.lintegral_eq_nnreal · cited by 6MeasureTheory.lintegral_e…MeasureTheory.SimpleFunc.approx · cited by 4SimpleFunc.approxMeasureTheory.SimpleFunc.measure_lt_top_of_memLp_indicator · cited by 3SimpleFunc.measure_lt_top…MeasureTheory.SimpleFunc.memLp_approxOn · cited by 3SimpleFunc.memLp_approxOnMeasureTheory.SimpleFunc.range_const · cited by 3SimpleFunc.range_constMeasureTheory.SimpleFunc.const_mul_lintegral · cited by 3SimpleFunc.const_mul_lint…MeasureTheory.lintegral_const_mul_le · cited by 2MeasureTheory.lintegral_c…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.SimpleFunc · cited by 411MeasureTheory.SimpleFuncSet.finite_range_const · cited by 0Set.finite_range_constSimpleFunc.constCITED BYCITES

Cites3

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Cited by53

Results whose statement or proof uses this declaration.