Theorems · Theorem · measure theory
ENNReal.tsum_eq_iSup_sum
∀ {α : Type u_1} {f : α → ENNReal}, ∑' (a : α), f a = ⨆ s, ∑ a ∈ s, f a- Cited by
- 10 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- iSupstatement · cited by 2,415
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- HasSum.tsum_eqproof · cited by 150
- ENNReal.hasSumproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_sum_measureproof · cited by 16
- MeasureTheory.lintegral_tsumproof · cited by 12
- Directed.measure_iUnionproof · cited by 5
- Measurable.ennreal_tsumproof · cited by 2
- MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint₀proof · cited by 2
- ENNReal.tsum_eq_iSup_sum'proof · cited by 2
- lowerSemicontinuousWithinAt_tsumproof · cited by 2
- AEMeasurable.ennreal_tsumproof · cited by 1
- MeasureTheory.tsum_measure_le_measure_univproof · cited by 1
- StieltjesFunction.length_subadditive_Icc_Iooproof · cited by 1