coe_expect — Mathlib

English

Real embedding commutes with the finite expectation operator: Real. toNNReal of an expectation equals the expectation of Real.toNNReal.

Русский

Преобразование Real commuting с ожиданием: Real.toNNReal(\\\\mathbb{E}_{i \\\\in s} f(i)) = \\\\mathbb{E}_{i \\\\in s} (f(i))^{\\\\toNNReal}.

LaTeX

$$$\\\\mathbb{E}_{i \\\\in s} f(i)^\uparrow = \\\\mathbb{E}_{i \\\\in s} (f(i)^\uparrow).$$$

Lean4

@[simp, norm_cast]
theorem coe_expect (s : Finset ι) (f : ι → ℝ≥0) : 𝔼 i ∈ s, f i = 𝔼 i ∈ s, (f i : ℝ) :=
  map_expect toRealHom ..

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