mconv_dirac_one — Mathlib

English

Another form of Dirac convolution: μ ∗ δ_x = μ.map (y ↦ y·x).

Русский

Другая форма свёртки с дирaком: μ ∗ δ_x = μ.map (y ↦ y·x).

LaTeX

$$$ μ ∗ δ_x = μ.map (\lambda y. y \cdot x) $$$

Lean4

/-- Convolution of a measure μ with the dirac measure at 1 returns μ. -/
@[to_additive (attr := simp) /-- Convolution of a measure μ with the dirac measure at 0 returns μ. -/
    ]
theorem mconv_dirac_one [MeasurableMul₂ M] (μ : Measure M) [SFinite μ] : μ ∗ₘ (dirac 1) = μ := by simp [mconv_dirac]

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