Skip to content

Commit

Permalink
feat(measure_theory/function/ae_eq_of_integral): remove a few unneces…
Browse files Browse the repository at this point in the history
…sary `@` (#11974)

Those `@` were necessary at the time, but `measurable_set.inter` changed and they can now be removed.
  • Loading branch information
RemyDegenne committed Feb 11, 2022
1 parent 114752c commit 1b78b4d
Showing 1 changed file with 5 additions and 5 deletions.
10 changes: 5 additions & 5 deletions src/measure_theory/function/ae_eq_of_integral.lean
Expand Up @@ -490,23 +490,23 @@ begin
have htf_zero : f =ᵐ[μ.restrict tᶜ] 0,
{ rw [eventually_eq, ae_restrict_iff' (measurable_set.compl (hm _ ht_meas))],
exact eventually_of_forall htf_zero, },
have hf_meas_m : @measurable _ _ m _ f, from hf.measurable,
have hf_meas_m : measurable[m] f, from hf.measurable,
suffices : f =ᵐ[μ.restrict t] 0,
from ae_of_ae_restrict_of_ae_restrict_compl _ this htf_zero,
refine measure_eq_zero_of_trim_eq_zero hm _,
refine ae_eq_zero_of_forall_set_integral_eq_of_sigma_finite _ _,
{ intros s hs hμs,
rw [integrable_on, restrict_trim hm (μ.restrict t) hs, measure.restrict_restrict (hm s hs)],
rw [← restrict_trim hm μ ht_meas, measure.restrict_apply hs,
trim_measurable_set_eq hm (@measurable_set.inter _ m _ _ hs ht_meas)] at hμs,
trim_measurable_set_eq hm (hs.inter ht_meas)] at hμs,
refine integrable.trim hm _ hf_meas_m,
exact hf_int_finite _ (@measurable_set.inter _ m _ _ hs ht_meas) hμs, },
exact hf_int_finite _ (hs.inter ht_meas) hμs, },
{ intros s hs hμs,
rw [restrict_trim hm (μ.restrict t) hs, measure.restrict_restrict (hm s hs)],
rw [← restrict_trim hm μ ht_meas, measure.restrict_apply hs,
trim_measurable_set_eq hm (@measurable_set.inter _ m _ _ hs ht_meas)] at hμs,
trim_measurable_set_eq hm (hs.inter ht_meas)] at hμs,
rw ← integral_trim hm hf_meas_m,
exact hf_zero _ (@measurable_set.inter _ m _ _ hs ht_meas) hμs, },
exact hf_zero _ (hs.inter ht_meas) hμs, },
end

lemma integrable.ae_eq_zero_of_forall_set_integral_eq_zero {f : α → E} (hf : integrable f μ)
Expand Down

0 comments on commit 1b78b4d

Please sign in to comment.