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affeldt-aist committed Feb 25, 2023
1 parent caa1f4b commit 31bc05c
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions theories/lebesgue_stieltjes_measure.v
Original file line number Diff line number Diff line change
Expand Up @@ -376,7 +376,7 @@ by rewrite -(hlength0 f) le_hlength//; exact: cumulative_is_nondecreasing.
Qed.

HB.instance Definition _ (f : cumulative R) :=
isAdditiveMeasure.Build _ R _ (hlength f : set ocitv_type -> _)
isContent.Build _ _ R (hlength f : set ocitv_type -> _)
(hlength_ge0' f) (hlength_semi_additive f).

Lemma hlength_content_sub_fsum (f : cumulative R) (D : {fset nat}) a0 b0
Expand All @@ -393,7 +393,7 @@ have mab k :
[set` D] k -> @measurable d itvs_semiRingOfSets `]a k, b k]%classic by [].
move: h; rewrite -bigcup_fset.
move/(@content_sub_fsum d R _
[the additive_measure _ _ of hlength f : set ocitv_type -> _] _ [set` D]
[the content _ _ of hlength f : set ocitv_type -> _] _ [set` D]
`]a0, b0]%classic (fun x => `](a x), (b x)]%classic) (finite_fset D) mab
(is_ocitv _ _)) => /=.
rewrite hlength_itv_bnd// -lee_fin => /le_trans; apply.
Expand All @@ -414,7 +414,7 @@ wlog wlogh : b A AE lebig / forall n, (b n).1 <= (b n).2.
set A' := fun n => if (b n).1 >= (b n).2 then set0 else A n.
set b' := fun n => if (b n).1 >= (b n).2 then (0, 0) else b n.
rewrite [X in (_ <= X)%E](_ : _ = \sum_(n <oo) hlength f (A' n))%E; last first.
apply: (@eq_eseries _ (hlength f \o A) (hlength f \o A')) => k.
apply: (@eq_eseriesr _ (hlength f \o A) (hlength f \o A')) => k.
rewrite /= /A' AE; case: ifPn => // bn.
by rewrite set_itv_ge//= bnd_simp -leNgt.
apply (h b').
Expand Down Expand Up @@ -476,7 +476,7 @@ Qed.
Let gitvs := [the measurableType _ of salgebraType ocitv].

Definition lebesgue_stieltjes_measure (f : cumulative R) :=
Hahn_ext [the additive_measure _ _ of hlength f : set ocitv_type -> _ ].
Hahn_ext [the content _ _ of hlength f : set ocitv_type -> _ ].

Let lebesgue_stieltjes_measure0 (f : cumulative R) :
lebesgue_stieltjes_measure f set0 = 0%E.
Expand Down

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