Theorems · Theorem · general topology

ENNReal.tendsto_const_sub_nhds_zero_iff

∀ {α : Type u_1} {l : Filter α} {f : α → ENNReal} {a : ENNReal},
  a ≠ ⊤ →
    (∀ (n : α), f n ≤ a) → (Filter.Tendsto (fun n => a - f n) l (nhds 0) ↔ Filter.Tendsto (fun n => f n) l (nhds a))

Defined in: Mathlib.Topology.Instances.ENNReal.Lemmas
Cited by: 1 results in Mathlib
Foundations: Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound

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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
Top.topstatement and proof · cited by 9,680
Filterstatement and proof · cited by 8,121
nhdsstatement and proof · cited by 5,554
Filter.Tendstostatement and proof · cited by 3,814
LE.le.transproof · cited by 3,151
Filter.Eventuallyproof · cited by 3,134
Set.Iccproof · cited by 1,702
Filter.univ_mem'proof · cited by 1,672
le_rflproof · cited by 1,558
Filter.mp_memproof · cited by 1,537
add_commproof · cited by 1,535

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.addContent_iUnion_eq_sum_of_tendsto_zeroproof · cited by 2