Is the skylight glass or plastic?
If the skylight glazing is plastic (either polycarbonate or acrylic), then it likely has a UV inhibitor that was included when the plastic was made, and that will prevent UV rays from passing thru the material.
The UV inhibitor is included in the plastic formulation to prevent the UV rays from the sun to degrade and eventually destroy the plastic. Both acrylics and polycarbonates are highly susceptible to UV damage when manufactured without the UV inhibitors.
If the skylight glazing is glass, then it is likely either tempered or laminated. If the skylight has laminated glass in its construction, then better than 99% of the UV rays are being blocked by the interlayer material used in manufacturing the glazing. This is similar to the UV inhibitors used in the manufacture of the plastic glazings.
If the skylight is glazed using tempered glass then it has no specific UV protection. While ordinary glass is opaque to UVB (which causes sunburn), it is transparent to UVA which is the UV that gives folks their nice golden tan (and is also likely the primary contributor to skin-cancer) and UVA is also the primary contributor to furniture and carpeting fading.
The glass in the skylight might have a LowE coating which will cut down on the UVA that passes thru the glass. The darker the coating, the greater the ability of the glazing to protect against fading damage. While UVA is the greater part of light-related fading problem, visible light also has some affect as well - it is a wavelength dependent issue.
There is equipment to measure how much UV is coming thru your windows, but as mentioned in a previous post it is expensive and not generally something to which a typical homeowner would have ready access.