Air does escape, in a small amount as it’s heated/sped up by energy from the sun, but mass is also added as the stellar wind collides with Earth and some of it slows down and is captured (for a while) by gravity. Water ice and bits of carbon-rich rock also fall into Earth and are vaporized before hitting the ground, adding to Earth’s atmosphere.
It’s not a closed system, but an ongoing one that is constantly seeking equilibrium between several different factors.
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