lmarginalPartialTraj — Mathlib

English

Evaluating lmarginalPartialTraj on a fixed x0 is equivalent to evaluating the corresponding measure map on the same x0.

Русский

Пре rendering lmarginalPartialTraj на фиксированном x0 эквивалентно вычислению соответствующей карты меры на той же x0.

LaTeX

$$$ lmarginalPartialTraj\,κ\,a\,c\;x_0 = \text{(map of partialTraj κ a c) on } x_0 $$$

Lean4

/-- This function computes the integral of a function `f` against `partialTraj`,
and allows to view it as a function depending on all the variables.

This is inspired by `MeasureTheory.lmarginal`, to be able to write
`lmarginalPartialTraj κ b c (lmarginalPartialTraj κ a b f) = lmarginalPartialTraj κ a c`. -/
noncomputable def lmarginalPartialTraj (a b : ℕ) (f : (Π n, X n) → ℝ≥0∞) (x₀ : Π n, X n) : ℝ≥0∞ :=
  ∫⁻ z : (i : Iic b) → X i, f (updateFinset x₀ _ z) ∂(partialTraj κ a b (frestrictLe a x₀))

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