Republican Michael R. Bloomberg defeated Democrat Mark Green in the race for New York City mayor Tuesday. Mr. Bloomberg, founder, president and CEO of Bloomberg LP, received 50% of the vote to Mr. Greens 47%. Mr. Bloomberg will succeed Rudolph W. Giuliani Jan. 1. Mr. Bloomberg becomes the first Republican ever to succeed another Republican mayor in the traditionally Democratic citys history. By some estimates, he spent up to $50 million of his own money in the race and received endorsements from Mr. Giuliani, New York Gov. George E. Pataki and former mayor Edward Koch.