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The phrase "within a time span of" is correct and is used in written English.
This phrase emphasizes the time limit or amount of time for something to occur. For example, "The project must be completed within a time span of one week."
Exact(23)
The beginning of the Mesozoic is a unique time in Earth history enduring two major mass extinctions within a time span of 40 million years.
Echostar-2's spin axis was observed to have moved approximately 180° in right ascension, within a time span of six months, suggesting a roughly one year spin axis precession period about the satellite's angular momentum vector.
Two palaeoenvironmental events occurred during the initial phase of the radiolarian extinction interval: (1) a post-impact shutdown of primary and biogenic silica production within a time span of 104 105 yr, and (2) a sustained reduction in the sinking flux of radiolarian silica for ~0.3 Myr after the impact.
Under these assumptions, sentence (19) says that Pollini played Opus 111 repeatedly within a time span of two weeks.
At the concentration of 500 mg/L, the degradation was about 85.6% within a time span of 14 days.
During my PhD, I tried to find out what factors caused some of the rapid climatic changes (i.e., changes from ice-age conditions to a present day climate within a time span of 5 to 25 years!) that have taken place over the past 16,000 years.
Similar(37)
All variables (n = 20) were calculated within a time-span of 500 ms (125 data frames) before ball release and 200 ms (50 data frames) after ball release.
If the tuff was emplaced separately, within a time span shorter than the standard deviation of the age dating, welded tuff at the summit area of Mt. Mudeung (>~1100 masl) could have been generated by tuff emplacement onto previously existing tuff emplacement (<~1100 masl) because the face widths of these colonnades are larger than those of the underlying colonnades.
I mean, isn't the challenge to agree to something that you can be held to, within a time span that people can adequately keep track of?
Within a longer time span of 8 years, Haukka et al. [ 6] calculated a suicide attempt incidence of 30% by using a nationwide study sample.
The constant comparative method of analysis was not possible because the interviews were conducted within a short time span of one week.
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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