mlconvolution_assoc — Mathlib

English

The mlconvolution operation is associative for measurable functions.

Русский

Операция mlconvolution существует ассоциативна для измеримых функций.

LaTeX

$$$f,g,k : G \\to \\mathbb{R}_{\\ge 0}^{\\infty},\\ hf hg hk \\Rightarrow f \\star_{μ} g \\star_{μ} k = (f \\star_{μ} g) \\star_{μ} k$$$

Lean4

@[to_additive /-- Convolution is associative. -/
    ]
theorem mlconvolution_assoc {f g k : G → ℝ≥0∞} (hf : Measurable f) (hg : Measurable g) (hk : Measurable k) :
    f ⋆ₘₗ[μ] g ⋆ₘₗ[μ] k = (f ⋆ₘₗ[μ] g) ⋆ₘₗ[μ] k :=
  mlconvolution_assoc₀ hf.aemeasurable hg.aemeasurable hk.aemeasurable

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