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Theorems · Theorem · measure theory

ENNReal.tsum_eq_zero

∀ {α : Type u_1} {f : α → ENNReal}, ∑' (i : α), f i = 0 ↔ ∀ (i : α), f i = 0
Defined in
Mathlib.Topology.Algebra.InfiniteSum.ENNReal
Cited by
3 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ENNReal.tsum_mul_left · cited by 21ENNReal.tsum_mul_leftMeasureTheory.Measure.MutuallySingular.sum_left · cited by 2MutuallySingular.sum_leftPMF.toOuterMeasure_apply_eq_zero_iff · cited by 1PMF.toOuterMeasure_apply_…ENNReal · cited by 9879ENNRealSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…tsum · cited by 1148tsumENNReal.summable · cited by 59ENNReal.summableSummable.tsum_eq_zero_iff · cited by 4Summable.tsum_eq_zero_iffENNReal.tsum_eq_zeroCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.