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Copula
.
Unique
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Imports
Init
Copula.Comonotonic
Copula.Independence
Copula.CDF.Extensionality
Mathlib.Tactic.FinCases
Imported by
ProbabilityTheory
.
Copula
.
instSubsingletonOfNatNat
ProbabilityTheory
.
Copula
.
cdf_dim_one
ProbabilityTheory
.
Copula
.
instSubsingletonOfNatNat_1
ProbabilityTheory
.
Copula
.
eq_independence_dim_one
ProbabilityTheory
.
Copula
.
independence_eq_comonotonic_dim_one
← Mathematical handbook
Uniqueness in dimensions zero and one
#
source
instance
ProbabilityTheory
.
Copula
.
instSubsingletonOfNatNat
:
Subsingleton
(
Copula
0
)
source
@[simp]
theorem
ProbabilityTheory
.
Copula
.
cdf_dim_one
(
C
:
Copula
1
)
(
u
:
Fin
1
→
↑
unitInterval
)
:
C
.
cdf
u
=
↑
(
u
0
)
source
instance
ProbabilityTheory
.
Copula
.
instSubsingletonOfNatNat_1
:
Subsingleton
(
Copula
1
)
source
theorem
ProbabilityTheory
.
Copula
.
eq_independence_dim_one
(
C
:
Copula
1
)
:
C
=
independence
1
source
theorem
ProbabilityTheory
.
Copula
.
independence_eq_comonotonic_dim_one
:
independence
1
=
comonotonic
1