It is in a scientific paper. I have a parameter V.

Is it 'for given V' or 'for a given V'?

I mean a given value of V, say, V=3. The full sentence is,

for given V, the function f(x;V) is always a convex function of x.

  • Please provide more context. What does V represent? Quote the full sentence with "given V". – laugh salutes Monica C Jul 19 '16 at 5:48
  • a: non-specific value, the: specific value Ex. For a given value V, X is always less than V*2. For the given value V=4, X is less than 8. – Leo Jul 19 '16 at 7:23

The usual phrase is

a given value


given values

which denotes the initial condition(s) of a calculation

for a given value of x
for given values of x

I think you might be trying to say

for given values of V, the function f(x;V) is always convex

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