Theorems · Theorem · general topology
NNReal.coe_tsum
∀ {α : Type u_2} {L : SummationFilter α} {f : α → NNReal}, ↑(∑'[L] (a : α), f a) = ∑'[L] (a : α), ↑(f a)- Defined in
- Mathlib.Topology.Instances.NNReal.Lemmas
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- tsumstatement · cited by 1,148
- SummationFilterstatement and proof · cited by 607
- Real.toNNReal_coeproof · cited by 36
- NNReal.continuous_coeproof · cited by 22
- continuous_real_toNNRealproof · cited by 15
- Function.LeftInverse.map_tsumproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- NNReal.summable_sigmaproof · cited by 7
- ENNReal.tsum_toReal_eqproof · cited by 3
- NNReal.tsum_mul_rightproof · cited by 2
- NNReal.tendsto_tsum_compl_atTop_zeroproof · cited by 1
- NNReal.tsum_mul_leftproof · cited by 0
- NNReal.coe_tsum_of_nonnegproof · cited by 0