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.
ENNRealExt
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Imports
Init
Mathlib.Topology.Algebra.InfiniteSum.ENNReal
Mathlib.Topology.Instances.ENNReal.Lemmas
Imported by
ENNReal
.
tsum_biUnion''
NNRat
.
ennreal_cast
NNRat
.
ennreal_cast_zero
NNRat
.
ennreal_cast_one
NNRat
.
toENNReal_sub
Extensions to
ENNReal
#
The intention is to upstream these to mathlib.
source
theorem
ENNReal
.
tsum_biUnion''
{
α
:
Type
u_2}
{
ι
:
Type
u_1}
{
t
:
ι
→
Set
α
}
{
f
:
↑
(⋃ (
i
:
ι
),
t
i
)
→
ENNReal
}
(
h
:
Set.univ
.
PairwiseDisjoint
t
)
:
∑'
(
x
:
↑
(⋃ (
i
:
ι
),
t
i
)
)
,
f
x
=
∑'
(
i
:
ι
) (
x
:
↑
(
t
i
)
)
,
f
⟨
↑
x
,
⋯
⟩
source
@[simp]
theorem
NNRat
.
ennreal_cast
{
n
:
ℕ
}
:
↑
↑
n
=
↑
n
source
@[simp]
theorem
NNRat
.
ennreal_cast_zero
:
↑
0
=
0
source
@[simp]
theorem
NNRat
.
ennreal_cast_one
:
↑
1
=
1
source
@[simp]
theorem
NNRat
.
toENNReal_sub
(
a
b
:
ℚ≥0
)
:
↑(
a
-
b
)
=
↑
a
-
↑
b