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Let be a distribution function.
Let be a distribution function such that and.
Let be a distribution function on such that and for all.
Theorem 2. Let F be a distribution function such that 1 - ( 1 - ȳ ) 2 + σ 2 < y m < ȳ.
Let D be a distribution function defined by D t)= textstylebegin{cases}0 &(tleq0), cr 1-e^{-t} &(t>0).
Let Ψ be a distribution function on X × X × [ 0, ∞ ] such that Ψ (x, y, ·) is symmetric, nondecreasing and Ψ ( c x, c x, t ) ≥ Ψ x, x, t | c | ( x ∈ X, c ≠ 0 ).
Similar(51)
This shows that (D^_{A}(t)) is a distribution function.
First, we prove that (widetilde{G}^) is a distribution function.
If F is a distribution function which satisfies F ( 0 ) = 0, then F is called a nonnegative distribution function.
If A is a generalized probabilistically bounded set, then (D^_{A}) is a distribution function.
(1) If A is a generalized probabilistically bounded set, then (D^_{A}) is a distribution function.
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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.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com