The moon could theoretically keep an Earth density atmosphere, but only for a fairly short time of maybe 1000 years or so. However, even if that could somehow be achieved there would still be some problems. For example, in longest days of the night, the atmosphere might freeze. It would also have a high wind volume, at the day/night terminator. It would lose a lot of its atmosphere due to Solar Wind and simple lose by having too much energy.
The moon could theoretically keep an Earth density atmosphere, but only for a fairly short time of maybe 1000 years or so. However, even if that could somehow be achieved there would still be some problems. For example, in longest days of the night, the atmosphere might freeze. It would also have a high wind volume, at the day/night terminator. It would lose a lot of its atmosphere due to Solar Wind and simple lose by having too much energy.