Theorems · Theorem · general topology
BoundedContinuousFunction.coe_prod
∀ {α : Type u} {R : Type u_2} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace R] {ι : Type u_3} (s : Finset ι)
[inst_2 : CommMonoid R] [inst_3 : BoundedMul R] [inst_4 : ContinuousMul R] (f : ι → BoundedContinuousFunction α R),
⇑(∏ i ∈ s, f i) = ∏ i ∈ s, ⇑(f i)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- PseudoMetricSpacestatement and proof · cited by 1,550
- BoundedContinuousFunctionstatement and proof · cited by 511
- ContinuousMulstatement and proof · cited by 343
- map_prodproof · cited by 108
- BoundedMulstatement and proof · cited by 14
- BoundedContinuousFunction.coeFnMonoidHomproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunctionproof · cited by 4
- indicator_indepFun_pi_of_bcfproof · cited by 2
- indepFun_pi_of_bcfproof · cited by 1
- Measure.ext_of_integral_mul_prod_boundedContinuousFunction'proof · cited by 1
- Measure.ext_of_integral_prod_mul_boundedContinuousFunction'proof · cited by 1
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunction'proof · cited by 1
- pi_indepFun_of_bcfproof · cited by 1
- pi_indepFun_pi_of_bcfproof · cited by 1
- BoundedContinuousFunction.prod_applyproof · cited by 0