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minor fix
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affeldt-aist committed Jan 3, 2025
1 parent c48e72f commit 9f5064f
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4 changes: 2 additions & 2 deletions theories/kernel.v
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Expand Up @@ -1566,14 +1566,14 @@ Definition mkproduct :=

End kproduct_measure.

(* [Theorem 14.22, Klenke 2014] (3/3): the composition of finite transition
kernels is sigma-finite *)
HB.instance Definition _ d0 d1 d2 (T0 : measurableType d0)
(T1 : measurableType d1) (T2 : measurableType d2) {R : realType}
(k1 : R.-ftker T0 ~> T1) (k2 : R.-ftker (T0 * T1) ~> T2) :=
@isKernel.Build _ _ T0 (T1 * T2)%type R
(mkproduct k1 k2) (measurable_kproduct k1 k2).

(* [Theorem 14.22, Klenke 2014] (3/3): the composition of finite transition
kernels is sigma-finite *)
Section sigma_finite_kproduct.
Context d0 d1 d2 (T0 : measurableType d0)
(T1 : measurableType d1) (T2 : measurableType d2) {R : realType}
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2 changes: 1 addition & 1 deletion theories/lebesgue_integral.v
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Expand Up @@ -5950,7 +5950,7 @@ Context d d' (X : measurableType d) (Y : measurableType d') (R : realType).
Variables (m1 : {sfinite_measure set X -> \bar R}).
Variables (m2 : {sfinite_measure set Y -> \bar R}).
Variables (f : X * Y -> \bar R) (f0 : forall xy, 0 <= f xy).
Hypothesis mf : measurable_fun setT f.
Hypothesis mf : measurable_fun [set: X * Y] f.

Lemma sfinite_Fubini :
\int[m1]_x \int[m2]_y f (x, y) = \int[m2]_y \int[m1]_x f (x, y).
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4 changes: 2 additions & 2 deletions theories/prob_lang.v
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Expand Up @@ -1466,8 +1466,8 @@ by rewrite /score/= /mscale/= ger0_norm//= f0.
Qed.

Lemma score_score (f : R -> R) (g : R * unit -> R)
(mf : measurable_fun setT f)
(mg : measurable_fun setT g) :
(mf : measurable_fun [set: R] f)
(mg : measurable_fun [set: R * unit] g) :
letin (score mf) (score mg) =
score (measurable_funM mf (measurableT_comp mg (measurable_pair2 tt))).
Proof.
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