"measure" is OK with words like "level", "standard", "quality", etc.. "determine" and "assess" would also work. "measure the English of someone" doesn't sound quite right.
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Hole One a New See Sometimes I would appreciate if monolingual dictionaries were more detailed (for example they leave out the 'quality' thing [it is in the etc. part but it should be written down explicitly]).If they told us every possible way in which a word can be used, the entry for each word would be many pages long. My Oxford English Dictionary has 21,
I could imagine it as:
to judge the importance, value or effect of something