const — Mathlib

English

The set { x | leftLim f x ≠ f x } is countable for a fixed Stieltjes function f.

Русский

Множество {x | leftLim f x ≠ f x } счетно по объединению.

LaTeX

$$$$ \\{ x \\mid \\text{leftLim } f x \\neq f x \\} \\text{ is countable. }$$$$

Lean4

/-- Constant functions are Stieltjes function. -/
protected def const (c : ℝ) : StieltjesFunction
    where
  toFun := fun _ ↦ c
  mono' _ _ := by simp
  right_continuous' _ := continuousWithinAt_const

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