dirac_eq_dirac_iff — Mathlib

English

Equality of Dirac measures is equivalent to equality of their centers.

Русский

Равенство мер Дирака эквивалентно равенству точек-центров.

LaTeX

$$$\\mathrm{dirac}_x = \\mathrm{dirac}_y \\iff x = y$$$

Lean4

/-- Dirac delta measures at two points are equal if and only if the two points are equal,
assuming the measurable space separates points. -/
theorem dirac_eq_dirac_iff [SeparatesPoints α] {x y : α} : Measure.dirac x = Measure.dirac y ↔ x = y :=
  not_iff_not.mp dirac_ne_dirac_iff

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