To begin with, an atmosphere mostly consists of gas molecules. As the moon have a weak gravitational field, the velocity required by the gas molecules to escape its gravitational reach will be much lesser. Also, it is found that the velocity of the gas molecules generally present in our atmosphere is more than that required to leave the moon's gravitational field. Or if any of the gas molecules will be present there, they will escape its gravitational field as their velocity is greater than the escape velocity of the moon.
In short we can say that as the gravitational field of the moon is weak, it is unable to hold the gas molecules around itself as an atmosphere.
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