expect_boole_mul' — Mathlib

English

A variant of Boole-type averaging: E_{j} ite(j=i) (|ι|).cast 0 · f(j) = f(i).

Русский

Вариант булевой усреднения: E_{j} 1_{j=i} (|ι|).cast 0 · f(j) = f(i).

LaTeX

$$$\mathbb{E}_{j\in ι} \big( \mathbf{1}_{j=i} \cdot (|ι|)^{\text{cast}} \cdot 0 \cdot f(j) \big) = f(i).$$$

Lean4

theorem expect_boole_mul' [Fintype ι] [Nonempty ι] [DecidableEq ι] (f : ι → M) (i : ι) :
    𝔼 j, ite (j = i) (Fintype.card ι : M) 0 * f j = f i := by simp_rw [@eq_comm _ _ i, expect_boole_mul]

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