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IshiguroYoshihiro authored and affeldt-aist committed Dec 21, 2023
1 parent 4bddc61 commit f849d9a
Showing 1 changed file with 6 additions and 2 deletions.
8 changes: 6 additions & 2 deletions theories/charge.v
Original file line number Diff line number Diff line change
Expand Up @@ -479,7 +479,10 @@ HB.instance Definition _ := isCharge.Build _ _ _
End pushforward_charge.

HB.builders Context d (T : measurableType d) (R : realType)
mu of Measure_isFinite d T R mu.
(mu : set T -> \bar R) of Measure_isFinite d T R mu.

Let mu0 : mu set0 = 0.
Proof. by apply: measure0. Qed.

HB.instance Definition _ := isCharge.Build _ _ _
mu (measure0 [the content _ _ of mu]) fin_num_measure measure_semi_sigma_additive.
Expand Down Expand Up @@ -970,7 +973,8 @@ HB.instance Definition _ := @Measure_isFinite.Build _ _ _
jordan_neg finite_jordan_neg.

Lemma jordan_decomp (A : set T) (mA : measurable A) :
nu A = (cadd [the charge _ _ of jordan_pos] [the charge _ _ of (cscale (-1) [the charge _ _ of jordan_neg])]) A.
nu A = (cadd [the charge _ _ of jordan_pos]
([the charge _ _ of cscale (-1) [the charge _ _ of jordan_neg]])) A.
Proof.
rewrite caddE cjordan_posE /= cscaleE EFinN mulN1e cjordan_negE oppeK.
rewrite /crestr0 mem_set// -[in LHS](setIT A).
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