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rename cumulative
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theories/lebesgue_stieltjes_measure.v

Lines changed: 6 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -601,15 +601,15 @@ Hint Extern 0 (measurable [set _]) => solve [apply: measurable_set1] : core.
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Hint Extern 0 (measurable [set` _] ) => exact: measurable_itv : core.
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HB.mixin Record isCumulativeBounded (R : numFieldType) (l r : R) (f : R -> R) := {
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cumulativeNy0 : f @ -oo --> l ;
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cumulativey1 : f @ +oo --> r }.
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cumulativeNy : f @ -oo --> l ;
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cumulativey : f @ +oo --> r }.
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#[short(type=cumulativeBounded)]
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HB.structure Definition CumulativeBounded (R : numFieldType) (l r : R) :=
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{ f of isCumulativeBounded R l r f & Cumulative R f}.
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Arguments cumulativeNy0 {R l r} s.
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Arguments cumulativey1 {R l r} s.
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Arguments cumulativeNy {R l r} s.
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Arguments cumulativey {R l r} s.
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Section probability_measure_of_lebesgue_stieltjes_mesure.
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Context {R : realType} (f : cumulativeBounded (0:R) (1:R)).
@@ -629,9 +629,9 @@ have : (lsf \o I) n @[n --> \oo] --> 1%E.
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by rewrite wlength_itv_bnd// ge0_cp.
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rewrite -(sube0 1); apply: cvgeB => //.
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- by apply/cvg_EFin; [near=> F
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|exact/(cvg_comp _ _ (@cvgr_idn R))/cumulativey1].
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|exact/(cvg_comp _ _ (@cvgr_idn R))/cumulativey].
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- apply/cvg_EFin; [by near=> F|apply: (cvg_ninftyP _ _).1 => //].
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exact: cumulativeNy0.
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exact: cumulativeNy.
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by apply: (cvg_comp _ _ (@cvgr_idn R)); rewrite ninfty.
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have : (lsf \o I) n @[n --> \oo] --> lsf (\bigcup_n I n).
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apply: nondecreasing_cvg_mu; rewrite /I//; first exact: bigcup_measurable.

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