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The phrase "on territory" is correct and usable in written English.
It can be used to refer to a specific area or land, often in contexts related to geography, law, or military.
Example: "The negotiations took place on territory that both countries claimed as their own."
Alternatives: "in the area" or "within the region".
Exact(59)
From then on, territory seized by conquest in a war of aggression wasn't exempt from reparations.
Iran, whose President Mahmoud Ahmadinejad considers Israel an illegitimate state established on territory stolen from Palestinians, was quick to deny any contact whatsoever.
The Warnockian style is one based on territory and set pieces, with the direct pass most often the most effective method of securing favourable pitch position.
Rural America has the edge on territory.
Both sides were to exchange "comprehensive proposals on territory and security" within three months.
Often the guerrillas melted away, to fight another day on territory of their own choosing.
The Pakistani Taliban retained a grip on territory running along the border with Afghanistan.
As a result, they sometimes encroach on territory private-equity firms consider their own.
Yet this year they have not managed to extend their hold on territory.
They sit cheek by jowl on territory not much bigger than a place mat.
To compromise on territory might seem, under certain conditions, imperative or at least politically expedient.
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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