Theorems · Theorem · measure theory
ENNReal.tsum_eq_liminf_sum_nat
∀ {f : ℕ → ENNReal}, ∑' (i : ℕ), f i = Filter.liminf (fun n => ∑ i ∈ Finset.range n, f i) Filter.atTop- Cited by
- 1 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- Filter.atTopstatement · cited by 2,405
- SummationFilter.unconditionalstatement · cited by 2,068
- Finset.rangestatement · cited by 1,341
- tsumstatement · cited by 1,148
- Filter.liminfstatement · cited by 198
- Summable.hasSumproof · cited by 184
- ENNReal.summableproof · cited by 59
- HasSum.tendsto_sum_natproof · cited by 23
- Filter.Tendsto.liminf_eqproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.isSFiniteKernel_withDensity_of_isFiniteKernelproof · cited by 0