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"incapability of" is correct and usable in written English.
It is usually used to refer to the inability of someone or something to do something, usually due to a lack of skill or resources. For example, "His incapability of understanding the physics concepts led him to fail the exam."
Exact(60)
Then there is the incapability of the authorities to deal with anything of this magnitude," says Dr Pervez.
Was this punishment for Greece's apparent incapability of securing her maritime borders, for her policy of waving refugees through, for her lack of cooperation?
As early as 1936, at the age of nineteen, she wrote to a friend, "The incapability of mine to 'act' is spreading.
"It's another case showing the politicization of the justice system in Mexico and the incapability of having due process," he said.
"The central idea pervading this struggle," Lincoln said in 1861, "is the necessity … of proving that popular government is not an absurdity," for "if we fail it will go far to prove the incapability of the people to govern themselves".
"It's not up to fans really to make statements about management decisions but it does show the incapability of the club's owners, even after two years, repeating the same mistakes.
Therefore, in some cases the incapability of the process is the effect of incapability of its preceding processes.
One is its incapability of handling with random preference discrepancies, the other is its incapability of finding out the correlative factors with panel data.
It shows that the incapability of the process in the second stage is the effects of the incapability of the process in the first stage.
In 802.11aa-2012, despincapabilitylity of packet-level differentiation, credit-based scheduling is recommended by default.
This can be due to the incapability of those needing the services to pay for them.
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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