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The phrase "is pervading" is correct and usable in written English.
It often indicates that something is "becoming more widespread or pervasive". For example, "A sense of fear is pervading the city following the increase in crime rate."
Dictionary
is pervading
verb
To be in every part of; to spread through.
Exact(16)
AN AIR of impending doom is pervading the senior common rooms of Britain's top two universities.
THE stench of vested interest is pervading Japan's continued restriction on the use of the contraceptive pill.
But the contests are the latest example of how technology is pervading the lives of children in ways that parents and teachers struggle to understand or monitor.
The clothes themselves followed the sports theme that is pervading the spring/summer 2014 shows, but the dynamism and the imagination of the designer was the greatest achievement of the show.
It's a thoughtful line of inquiry for Google to be pursuing, and highly relevant as well, considering how machine learning is pervading so many industries so quickly.
Information about the youngest Windsor is pervading the atmosphere, like the ashes of that Icelandic volcano that filled up the sky a few summers ago, grounding flights worldwide.
Similar(44)
Unlike the meretricious "Life Is Beautiful," "Divided We Fall" is pervaded with humor that serves not to sentimentalize or sugarcoat the monstrosity of Naziism, but to explain it.
Everyday modern life is pervaded by electromagnetic phenomena.
Besides irony, Papageorge's photography is pervaded by sensuality.
The portrait is pervaded by a sense of loneliness and isolation.
Unlike the first symphony in mood, it is pervaded in all movements by optimistic calm.
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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