Banshee's Veil and Guardian angel is good too!
Many people using jax liks Hextech Gunblade but i dont so it just me.

My game usually end by atmas, I have yet to see a team survive against my late game jax besides Atlanta's warwick etc. or my team lost the game before it starts etc etc.
Basically max leap while having all the skills. Then empower, then dodge.
This is more offensive and is more effective because you can not only farm faster, but do more dmg etc. endgame etc.

1.1.He can leap on wards. (My own little discovery which means you can escape easier, for those who didn't know)
2.Atmas is a good item AFTER guinsoo's rage blade, not a good first item.
3.Attack dmg Jax does not mean you get Rylai's dumbass
4.Red and Blue Elxier after having atmas and rage blade is ridiculous. At lvl 15 you have a potential 4000 hp.
5.You can Rally and walk in and out and regen your hp through the passive.

Don't just copy my item build, make your own to your play style