continuous_mulIndicator — Mathlib

English

The constant-one function is Multipliable with respect to any summation filter L.

Русский

Постоянно единичная функция является Multipliable по отношению к любому фильтру суммирования L.

LaTeX

$$$\\text{Multipliable } (\\lambda _ \\to 1)\\ L$$$

Lean4

@[to_additive]
theorem continuous_mulIndicator (hs : ∀ a ∈ frontier s, f a = 1) (hf : ContinuousOn f (closure s)) :
    Continuous (mulIndicator s f) := by classical exact continuous_piecewise hs hf continuousOn_const

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