This is the build that I have come up with for Dominion, but obviously varies depending on how you play Jax. With this build I concentrate on quickly eliminating the casters and weaker AD Supports. The speed as well as the focus on his stun allows you to harass a lot more effectively without giving up the ability to stomp on your opponents. Because of Jax's Ulty as well as the life steel you aren't giving up that much durability.

The build may vary also depending on how many tanks, support tanks or other champions that are in the arena. Other good items for those scenarios include: Last Whisper, Hextech Gunblade for more AP damage and sustainability.