If i hold a glass full of air upside down, and i take it to the bottom of the swimming pool without tipping it, the density (thickness) of the air inside the glass will be at the surface.

The answer to fill in the blank in the question above is "greater than" based on the physic of the air density. The density of air is affected by the temperature and the pressure based on the ideal gas law. A high pressure will make the air becomes denser and the bottom of swimming pool has a higher pressure than the surface.