Theorems · Theorem · measure theory
measurableSet_uIoc
∀ {α : Type u_1} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [OpensMeasurableSpace α] [inst_2 : LinearOrder α]
{a b : α} [ClosedIicTopology α], MeasurableSet (Set.uIoc a b)- Cited by
- 20 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- LinearOrderstatement and proof · cited by 8,572
- MeasurableSetstatement · cited by 3,075
- OpensMeasurableSpacestatement and proof · cited by 636
- Set.uIocstatement · cited by 182
- ClosedIicTopologystatement and proof · cited by 115
- measurableSet_Iocproof · cited by 65
Cited by20
Results whose statement or proof uses this declaration.
- intervalIntegral.intervalIntegrable_cpow'proof · cited by 7
- Real.circleAverage_congr_codiscreteWithinproof · cited by 4
- intervalIntegrable_congrproof · cited by 4
- intervalIntegral.tendsto_integral_filter_of_dominated_convergenceproof · cited by 3
- intervalIntegral.integral_congr_codiscreteWithinproof · cited by 2
- intervalIntegral.hasSum_integral_of_dominated_convergenceproof · cited by 2
- exists_eq_interval_average_of_nullSingletonClassproof · cited by 2
- TendstoUniformlyOn.tendsto_intervalIntegral_of_continuousOnproof · cited by 1
- not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_auxproof · cited by 1
- intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_leproof · cited by 1
- Polynomial.mahlerMeasure_le_sqrt_sum_sq_norm_coeffproof · cited by 1
- exists_eq_const_mul_intervalIntegral_of_ae_nonnegproof · cited by 1