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The phrase "progress in improving" is correct and usable in written English.
It can be used when discussing advancements or developments in a particular area or field.
Example: "We have made significant progress in improving our customer service response times over the past year."
Alternatives: "advancements in enhancement" or "improvements in development."
Exact(60)
But there has been real progress in improving safety.
Teachers said a change to pensions could erode the considerable progress in improving recruitment.
"There's real good progress in cash flow and further progress in improving the balance sheet.
Transportation officials in the region say they are making incremental progress in improving road conditions.
The city has already made progress in improving reading performance for children in the lower grades.
Today, administration officials said this did not mean unfettered progress in improving those relations.
But the UK's recent progress in improving the wellbeing of its citizens was much weaker.
The bank said it had made "significant progress" in improving its capital and liquidity positions.
The group named companies making "significant progress" in improving welfare standards of hens.
Progress in improving environmental conditions around the monument has been slow, however.
The government has made little progress in improving its fiscal position.
More suggestions(16)
achievement in improving
headway in improving
progress in ameliorating
progress in boosting
work in improving
progress in alleviating
stage in improving
progress in achieving
breakthroughs in improving
accomplishments in improving
strides in improving
inroads in improving
making in improving
made in improving
achievements in improving
progress in improvement of
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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