Theorems · Theorem · measure theory
ENNReal.sum_le_tsum
∀ {α : Type u_1} {f : α → ENNReal} (s : Finset α), ∑ x ∈ s, f x ≤ ∑' (x : α), f x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 130 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 and proof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- zero_leproof · cited by 382
- ENNReal.summableproof · cited by 59
- Summable.sum_le_tsumproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- ENNReal.tsum_const_eq_top_of_ne_zeroproof · cited by 4
- MeasureTheory.Content.innerContent_iSup_natproof · cited by 3
- MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRingproof · cited by 2
- ENNReal.le_tsum_of_forall_lt_exists_sumproof · cited by 1
- ENNReal.le_tsum_schlomilchproof · cited by 1
- ENNReal.tsum_schlomilch_leproof · cited by 1
- MeasureTheory.Measure.InnerRegularWRT.weaklyRegular_of_finiteproof · cited by 1
- ENNReal.le_tsum_condensedproof · cited by 0
- ENNReal.tsum_condensed_leproof · cited by 0
- ENNReal.finset_card_const_le_le_of_tsum_leproof · cited by 0