Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.FinMeasSupp.of_lintegral_ne_top
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : MeasureTheory.SimpleFunc α ENNReal},
f.lintegral μ ≠ ⊤ → f.FinMeasSupp μ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- LT.lt.neproof · cited by 872
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- Finset.mem_insert_selfproof · cited by 128
- MeasureTheory.SimpleFunc.rangeproof · cited by 97
- MeasureTheory.SimpleFunc.lintegralstatement and proof · cited by 55
- Finset.subset_insertproof · cited by 36
- MeasureTheory.SimpleFunc.FinMeasSuppstatement · cited by 18
- MeasureTheory.SimpleFunc.finMeasSupp_iffproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.measure_support_lt_top_of_lintegral_ne_topproof · cited by 1
- MeasureTheory.exists_setLIntegral_compl_ltproof · cited by 1
- MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_memLpproof · cited by 1
- MeasureTheory.SimpleFunc.FinMeasSupp.iff_lintegral_lt_topproof · cited by 0