Exact(35)
Noting that R is a doubling ball we have R = R ˜.
They work under the assumption that ϕ is subharmonic and that (Deltaphi, dA) is a doubling measure, where dA is the area measure on ({mathbb {C}}).
If μ is a doubling measure, then ∥ f ∥ L p, ν ; k ( G ) and ∥ f ∥ L p, ν ; 1 ( G ) are equivalent for all p ≥ 1, k > 0 and ν > 0. .
Since vdσ is a doubling measure, from (3.9), there exists a constant C p,q such that u ( E ) ≤ C p, q λ p ∕ q ∫ S f p ∕ q v d σ.
(W in B_{q}) is a doubling measure, that is, there exists a constant (C>0) such that int_{B x,2r)}W y),mathrm{d}y leq C int_{B x,r)} W y),mathrm{d}y.
Let (Theta=Theta(r)), (r>0), be a growth function; that is, a positive increasing function on ((0,+infty)) and satisfy the following doubling condition: Theta(2r)leq DcdotTheta(r), quadmbox{for all } r>0, (2.7) where (D=D(Theta ge1) is a doubling constant independent of r. [8].
Similar(25)
This is a double whammy.
What is a double standard?
Mine is a double slipper.
Here is a double helping.
Which is a double tragedy.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

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