Air Purifiers

My apartment is 883 sq feet. I have 5 cats and there are lots of trees around the complex. I am not allergic to dust, tree or flower pollen or anything like that. My problem is all the freaking cat hair that ends up resting on my stuff and also all the general dust. The cat hair issue extends to where when I walk outside, cat hair is floating in the air of my apartment &
ends up on my clothes………I have lint rollers in the car.

I need something that:
* Freshens the air
* Dramatically decreases the cat hair everywhere in my apartment
* Dramatically decreases the dust that ends up on my
electronics, book shelves, etc.

Any suggestions?