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The phrase "a definite increase in" is correct and usable in written English
It can be used when discussing a clear or noticeable rise in a particular metric or variable. Example: "The recent study showed a definite increase in the number of participants over the last year."
Exact(41)
There's a definite increase in skills".
"There's a definite increase in some and decreases in others.
"There is a definite increase in people being killed.
"There's been a definite increase in fasting," said Kim Bobo, executive director of the National Interfaith Committee for Worker Justice.
"There has been a definite increase in traffic the last several months, clientele looking at the buildings," Mr. Ramat said.
"But there is also a definite increase in need," says Jeremy Ravn, the charity's food bank network director.
Similar(19)
Mutants V180I, T183A and T188K show a definite increase of flexibility in both the 165 175 and the 185 200 regions [Figure 2C].
This restructuring coincided with a time trend towards less advanced tumors being diagnosed, where a small but definite increase in women with localized disease and a corresponding decrease in women with regional disease over the study period were observed in Singapore (Table 1).
And this is a definite increase over past years.
Likewise, the incidence of anal cancer and anal intraepithelial neoplasia (AIN), the potential precursor lesion of squamous cell carcinoma of the anus is very high among HIV+ MSM [ 12] and a definite increasing trend in the incidence of anal cancer has been shown despite the use of Highly Active Antiretroviral Therapy (HAART) [ 13].
What is more, most could boast -- especially Zogby and CBS News -- that they picked up a slight but definite increase in support for Mr. Gore in the final 24 hours or so of the campaign.
More suggestions(20)
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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