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The phrase "a day on which" is correct and usable in written English.
It can be used to specify a particular day when an event occurs or is expected to occur.
Example: "We will celebrate our anniversary on a day on which the weather is pleasant."
Alternatives: "a day that" or "a day when".
Exact(56)
In the 2,358 infants with at least one apnea event recorded, 8,960 apnea event-days (a day on which at least one apnea event was recorded) were recorded in 111,298 total person-days in the analysis.
The C57Bl/CRL females with B16F1 tumours received glucose+MIBG on two consecutive days followed by a day on which only glucose was administered at a dose of 3 g kg−1.
Mr. Niederauer, who heads the exchange, had one of his officials do the job, officially ending a day on which the Dow Jones industrial average plummeted 778 points.
The Tiberius expedition was "a day on which Graham's good spirits held up throughout.
On Friday, a day on which the market tumbled, ratings for business news channels spiked.
But for Benitez, this was a day on which the possibilities seemed endless.
French authorities initially gave each Hmong a few dozen francs a day on which to survive.
A day on which the economic recession deepens still further is not a day to indulge in false optimism.
After a day on which many officers were concealing their identity badges, the Met dragged its heels.
Yesterday was the last day for the October futures contract, a day on which trading is often volatile.
The White House said "the world is watching" after a day on which at least 278 people were killed.
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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