Mayor Bloomberg is off to Los Angeles on Friday to share some of his New York City know-how with the new mayor of Los Angeles, Antonio Villaraigosa.

Mr. Villaraigosa, a Democrat who will be the first Hispanic mayor of Los Angeles since 1872, asked Mr. Bloomberg, a Republican, to attend his inauguration tomorrow. Mr. Bloomberg told reporters yesterday that while he’s in California, he will give the new mayor some pointers.

Mr. Bloomberg said he would like to develop a relationship with the new mayor of Los Angeles so that the two cities can work together in the future.

Mr. Bloomberg will attend the inauguration on his way to Singapore, where he is headed with the NYC2012 Olympic bid.

One of Mr. Bloomberg’s Democratic opponents in the mayoral race, Fernando Ferrer, is also attending Mr. Villaraigosa’s inauguration ceremony.

***

Picking up the endorsement of a onetime opponent, mayoral candidate Fernando Ferrer received yesterday the backing of Ruth Messinger, a former Manhattan borough president. Ms. Messinger and Mr. Ferrer – a former Bronx borough president – were rivals in the 1997 Democratic mayoral primary before Mr. Ferrer dropped out in May that year.

Ms. Messinger went on to lose heavily to Mayor Giuliani in the November general election.

The Messinger nod was a “paper endorsement” sent out by the Ferrer campaign late yesterday afternoon. At a private “Women for Ferrer” meeting yesterday morning, however, sponsored by Ms. Messinger and former Democratic vice-presidential candidate Geraldine Ferraro, Ms. Messinger said she was “proud to support Freddy” and praised Mr. Ferrer’s record. The breakfast gathering at which Ms. Messinger made her laudatory comments was closed to the press, but was attended by “special guest” and abortion activist Kate Michelman, president emeritus of the National Abortion and Reproductive Rights Action League.