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The phrase "a given dimension" is correct and usable in written English.
It can be used when referring to a specific measurement or aspect of an object or concept that has been predetermined or specified.
Example: "In this study, we will analyze the effects of temperature on the material properties in a given dimension."
Alternatives: "a specified dimension" or "a particular dimension".
Exact(37)
Fixed-type gauges are used to indicate whether a given dimension is larger or smaller than the standard.
To evaluate the computation results, proper physical model was built in a given dimension.
A single lower case bold letter x represents a column vector with a given dimension.
It would be of little interest if the addressing scheme could only serve frames of a given dimension.
Extension is not a determination of a dimension, but a determination of the entity that is extended in a given dimension.
In addition, the elements in a given dimension can be mapped in the increasing or decreasing order of the respective index.
Similar(23)
The ethical market adds a giving dimension to the everyday act of shopping.
The building itself is a box, a shed with given dimensions, topped with a roofscape of black and white boxes that spell out the MOMA brand.
They calculate what the ideal curvature should be for a rectangular sheet of given dimensions and thickness.
Triangle PQR conforms to the given dimensions.
Better was Phillip Ens as his evil henchman, Wurm, who wants Luisa for himself; Mr. Ens, looking like an unwashed Kevin Bacon, gave dimension to his character's despicability.
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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