Documentation
Carleson
.
ToMathlib
.
MeasureTheory
.
Function
.
LpSeminorm
.
TriangleInequality
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source
Imports
Init
Carleson.ToMathlib.Misc
Carleson.ToMathlib.MeasureTheory.Function.AEEqFun
Imported by
MemLp
.
toLp_sum
source
theorem
MemLp
.
toLp_sum
{
α
:
Type
u_1}
{
E
:
Type
u_2}
{
m0
:
MeasurableSpace
α
}
{
p
:
ENNReal
}
{
μ
:
MeasureTheory.Measure
α
}
[
NormedAddCommGroup
E
]
{
ι
:
Type
u_3}
(
s
:
Finset
ι
)
{
f
:
ι
→
α
→
E
}
(
hf
:
∀
i
∈
s
,
MeasureTheory.MemLp
(
f
i
)
p
μ
)
:
MeasureTheory.MemLp.toLp
(∑
i
∈
s
,
f
i
)
⋯
=
∑
i
:
↥
s
,
MeasureTheory.MemLp.toLp
(
f
↑
i
)
⋯