Can HEPA filtration reduce radon decay products?  Kind of.  Let's first outline in basic terms what radon is and why we should care.

Radon gas (Rn-222) is a radioactive isotope formed from the decay of uranium-238 that naturally occurs in the ground.  Radon is the most concerning byproduct of the uranium-238 decay because it is a gas and can get into the air in your home through the basement, crawl space, or any below ground part of the house.

Radon gas is dangerous because it radioactively decays to form radioactive metals such as polonium, lead, and bismuth.  When the radon and isotopes of polonium decay, they emit alpha particles that can damage DNA in your body.

Because radon is a gas, it decays in the air releasing the radioactive decay products where they can often attach to dust particulates in the air.  Any of these airborne decay products can be inhaled, where they further decay and release high energy alpha particles into the tissues of the lungs and can cause lung cancer.  Not good.

In fact, for most people radon gas accounts for more exposure to radioactivity than any other source.  It is also a leading source of lung cancer.

Some of the radon decay products are electrostatically attracted to tiny dust particulates in the air.  These are called attached radon decay products.  Air purifiers are not able to remove radon gas directly from the air.  However, a high quality HEPA filter in an air purifier can remove radioactive radon decay products that are attached to airborne particulates.

In this way, an air purifier with HEPA filtration can reduce the amount of radioactive decay products in the air in your home.  If you have high levels of radon, a radon mitigation system is still required.  A quality HEPA air purifier can help reduce any remaining radon decay products in the air before they have a chance to get into your lungs and cause damage.