Hochman is replacing outgoing D.A. George Gascón, who Nathan says was way too soft on violent and repeat offenders during his 4-year term ... and apparently voters agreed.

It's fitting ... Hochman says he's going to terminate a lot of the policies he calls lenient that Gascón was known for ... like not prosecuting drug possession and trespassing offenses ... and he's turning to the "Terminator" star -- and former California governor -- to get his first day in office started.

After being sworn in, Hochman addressed the crowd, saying ... "Blanket policies are inherently lazy. You have to look at each case individually -- the individual defendant and their background, the crime committed and the impact on the victim -- to determine who the true threats are to our public safety ... and the ones that aren't."

One of the first orders of business for Hochman will be reviewing the Menendez Brothers case.

Erik and Lyle are hoping to get out of prison ... either by resentencing, having their convictions changed from murder to manslaughter, or by clemency ... and Hochman told us last month he was ready to sink his teeth into the case.

Gascón supported resentencing, but last week a judge delayed a hearing on the matter until January, giving Hochman more time to review the case.