eapproxDiff — Mathlib

English

Definition of ennrealRatEmbed: a Nat → ENNReal map given by encoding nonnegative rationals.

Русский

Определение ennrealRatEmbed: отображение NAT → ENNReal через кодирование неотрицательных рациональных чисел.

LaTeX

$$$\text{ennrealRatEmbed}(n) := ENNReal.ofReal\left((Encodable.decode(\alpha := \mathbb{Q}, n)).getD(0)\right)$$$

Lean4

/-- Approximate a function `α → ℝ≥0∞` by a series of simple functions taking their values
in `ℝ≥0`. -/
def eapproxDiff (f : α → ℝ≥0∞) : ℕ → α →ₛ ℝ≥0
  | 0 => (eapprox f 0).map ENNReal.toNNReal
  | n + 1 => (eapprox f (n + 1) - eapprox f n).map ENNReal.toNNReal

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