Theorems · Theorem · general topology

tendsto_indicator_const_iff_tendsto_pi_pure

∀ {α : Type u_1} {A : Set α} {β : Type u_2} [inst : Zero β] [inst_1 : TopologicalSpace β] {ι : Type u_3} (L : Filter ι)
  {As : ι → Set α} [T1Space β] (b : β) [NeZero b],
  Filter.Tendsto (fun i => (As i).indicator fun x => b) L (nhds (A.indicator fun x => b)) ↔
    Filter.Tendsto (fun i x => x ∈ As i) L (Filter.pi fun x => pure (x ∈ A))

Defined in

Mathlib.Topology.IndicatorConstPointwise

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ZeroTopologicalSpaceT1SpaceNeZero