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.
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.
MeanInequalitiesPow
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Imports
Init
Mathlib.Analysis.MeanInequalitiesPow
Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality
Imported by
ENNReal
.
rpow_add_le_mul_rpow_add_rpow'
ENNReal
.
rpow_add_le_mul_rpow_add_rpow''
source
theorem
ENNReal
.
rpow_add_le_mul_rpow_add_rpow'
(
z₁
z₂
:
ENNReal
)
{
p
:
ℝ
}
(
hp
:
0
≤
p
)
:
(
z₁
+
z₂
)
^
p
≤
MeasureTheory.LpAddConst
(
ENNReal.ofReal
p
)
⁻¹
*
(
z₁
^
p
+
z₂
^
p
)
source
theorem
ENNReal
.
rpow_add_le_mul_rpow_add_rpow''
(
z₁
z₂
:
ENNReal
)
{
p
:
ENNReal
}
:
(
z₁
+
z₂
)
^
p
.
toReal
⁻¹
≤
MeasureTheory.LpAddConst
p
*
(
z₁
^
p
.
toReal
⁻¹
+
z₂
^
p
.
toReal
⁻¹
)