integrableExpSet — Mathlib

English

Under MemLp id 2 μ, the covariance bilinear dual equals the classical covariance functional: covarianceBilinDual μ L1 L2 = cov[L1, L2; μ].

Русский

При MemLp id 2 μ ковариационная билинейная двойка равна классической ковариационной функции: covarianceBilinDual μ L1 L2 = cov[L1,L2; μ].

LaTeX

$$$covarianceBilinDual(\\mu) L_1 L_2 = cov[L_1,L_2;\\mu]$$$

Lean4

/-- The interval of reals `t` for which `exp (t * X)` is integrable. -/
def integrableExpSet (X : Ω → ℝ) (μ : Measure Ω) : Set ℝ :=
  {t | Integrable (fun ω ↦ exp (t * X ω)) μ}

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