Theorems · Theorem · measure theory

StieltjesFunction.measure_Iio_of_tendsto_atBot_atBot

∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (f : StieltjesFunction R)
  [inst_2 : OrderTopology R] [inst_3 : CompactIccSpace R] [inst_4 : MeasurableSpace R] [inst_5 : BorelSpace R]
  [inst_6 : SecondCountableTopology R] [inst_7 : DenselyOrdered R],
  Filter.Tendsto (↑f) Filter.atBot Filter.atBot → ∀ (x : R), f.measure (Set.Iio x) = ⊤

Defined in: Mathlib.MeasureTheory.Measure.Stieltjes
Cited by: 1 results in Mathlib
Foundations: Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace OrderTopology CompactIccSpace MeasurableSpace BorelSpace SecondCountableTopology DenselyOrdered

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites36

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

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Realstatement · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Top.topstatement · cited by 9,680
LinearOrderstatement and proof · cited by 8,572
Filterproof · cited by 8,121
Bot.botproof · cited by 4,720
Filter.Tendstostatement and proof · cited by 3,814

Cited by1

Results whose statement or proof uses this declaration.

StieltjesFunction.measure_univ_of_tendsto_atBot_atBotproof · cited by 0