The task he faces is not easy. Mexico City is not only engulfed in a frightening crime wave but is also riddled with corruption and saturated with air pollution. Mr. Cardenas must also contend with soaring expectations among residents desperate for change.

A poll published this morning by the newspaper Reforma showed that 71 percent of city residents think that life in the capital will improve during his administration.

''We expect to see a change,'' said Gabriel Coleote Zayas, a 45-year-old merchant, as he stood earlier this week stirring pork rinds in a simmering vat of grease at his market stall in a working-class neighborhood. ''He is going to watch where our tax dollars go to see that they don't end up in the pockets of some bureaucrat.''

Florencio Rodriguez Perez, 62, a sidewalk photographer who has dressed up in a red plush Santa Claus suit for the Christmas season, reported glumly one day this week that he had three customers, who bought pictures worth only $2 each, in a whole day's work.

''We can't take any more lies and cheating from the city government,'' Mr. Rodriguez said, waiting beside an empty and forlorn-looking sleigh in a public square. ''We want Mr. Cardenas to keep the prices we pay for everything from going up and up. We want him to make more of an economy for poor people.''

Mr. Cardenas crushed his opponents in elections on July 6 by winning 47 percent of the vote. He will face no opposition from the City Council, since his left-of-center Party of the Democratic Revolution, or P.R.D., won 38 of the council's 66 seats.

But although his actions will be scrutinized in the national limelight, in practice Mr. Cardenas does not even control all of the metropolis for which the public will hold him responsible. As Mayor, he is in charge only of a federal district not unlike Washington, an urban core that encompasses only 40 percent of the Mexico City metropolitan area, which is home to 18.5 million people.