Gilbert Arenas -- Ex Demands Restraining Order ... Gilbert Claims Victory

Gilbert Arenas' ex demanded an emergency restraining order against him this week ... claiming he threatened her life ... but the judge shot her down ... TMZ Sports has learned.

It's no secret Gilbert and Laura Govan -- the mother of his 4 kids -- hate each other's guts. Arenas recently smashed the car she drives with a cinder block after she allegedly threw his computer in the pool.

Now, sources tell us ... Govan went to court this week telling the judge Gilbert threatened her on Monday -- allegedly saying, "I want you dead or in jail or broke."

Arenas obviously denied threatening her ... and the judge ultimately ruled there wasn't enough evidence to warrant an emergency restraining order.