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Some rioters stormed inside a Shell gas station on 5th Avenue and Olympic Boulevard, stealing thousands of dollars in merchandise.
"We lose about a total of $15,000 then," said owner Harry Hahn.
Police say surveillance video and photos posted on social networking sites helped them track down one of the alleged looters. Michael Rivas, 24, of Hawaiian Gardens, was arrested on Friday.
"Our detectives were able to identify him, reach out from downtown, pull him out and book him on a burglary charge," said LAPD Capt. Blake Chow.
Rivas was allegedly photographed loading boxes of energy drinks into a car.
"The individual may have been laughing on the video online but none of us are laughing here today," said Los Angeles City Councilwoman Jan Perry.
Police have photos and video of other suspects involved in the looting, and say they are determined to catch them.
"This is serious business," said LAPD Dep. Chief Sergio Diaz. "It may seem to these drunken fools that this is the thing to do if there's another victory to come downtown and cut up and act stupid. We're here to tell them, 'Don't do it.'"
Twenty arrests have been made for various offenses in connection with the looting and vandalism melee that occurred after the Lakers' victory.
The city of L.A. is offering a $10,000 reward for information leading to the arrest of others involved in criminal activity.