The most common and most likely answer to this crossword clue is the 8 letter word READINGS
I've seen this crossword clue in The Times
R
E
A
D
I
N
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S
More clues leading to the result READINGS
Buddy explains!

The straight part
We know that "measurements" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case measurements = readings.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does READINGS mean?
READINGS noun- The process of interpreting written language.
- The process of interpreting a symbol, a sign or a measuring device.
- A value indicated by a measuring device.
- An event at which written material is read aloud.
- An interpretation.
- Something to read; reading material.
- The extent of what one has read.
- (legislature) One of several stages a bill passes through before becoming law.
- A piece of literature or passage of scripture read aloud to an audience: readings from the Bible