Tuesday's election showed the District at its finest -- and the people in it at their most politically mature.

By electing Sharon Pratt Dixon, Eleanor Holmes Norton (despite misgivings) and Jesse L. Jackson, and rejecting Mayor Marion Barry's bid, the citizens not only signaled they wanted change but also demonstrated a feisty independence.

None of this could have happened had not voters felt a new entitlement -- a sense that, finally, they "own" this government. A scant 20 years ago, many Washington blacks felt too alienated to enter the District Building comfortably. Now they can weather an emotional crisis with their mayor, regroup and move ahead.

Ironically, that new spirit emerged partly because of the efforts of Dixon's two predecessors: Walter E. Washington and Barry.

It was in 1967, as riots were breaking out throughout the country, that President Lyndon B. Johnson directed that city government be reorganized to enable it to deal more effectively with segregation, poor housing, schools and joblessness. Washington, the public housing executive who became the first appointed mayor, took office seven months before the District exploded into riots after Dr. Martin Luther King Jr.'s assassination.

Washington steered the city through that crisis and its rank colonial relationship with Capitol Hill during that term and a second term as elected mayor. When the city once again felt the need for change, Washington was replaced by Barry.

While Barry's personal excesses and tragedies make it easy to forget his contributions, those contributions were real. They include the summer youth employment and youth leadership programs, improved services for the elderly, expanded minority participation in city contracts and projects, the expedited development of Pennsylvania Avenue and downtown Washington, and the influx of many talented people to government.

But ultimately, Barry's failings far outweighed his achievements -- at least in the minds of the electorate, which came out in record numbers. The voters Tuesday decided they had to be counted and wanted to participate in this change. The response to Dixon's "clean house" cry in the District primary and the turnout that gave her a landslide victory Tuesday were a measure of this thirst for change.

Dixon's win reflected a desire to move ahead on the city's pressing social and fiscal problems. Dixon's "We're going to clean house!" was an activist, we-are-in-charge slogan. It also was a far cry from the "We're-so-glad- to-have-a-black-in-charge" attitude of the Washington years, and the "We-don't-have-to-back-the-black-in-charge" attitude of Barry's final days. Moreover, it signaled a shift from the civil rights stance adopted in Barry's tenure in reaction to a segregationist past.

Now, all eyes will be on Dixon as she fills in her sketch of her vision for the city, makes key appointments and acts on campaign promises. That the talents of so many new elected officials are about to come to bear on the pressing problems of the city has engendered confidence and optimism in many citizens. On election night, Washingtonians danced with joy. Yesterday, the airwaves crackled with callers congratulating Dixon as she made the round of radio talk shows.

But as Dixon and others begin to act, I would like to see city residents exhibit the same good judgment they exhibited Tuesday as they come up with a vision for their role as citizens.

Almost half the young people in this city are in trouble -- dropping out of school and becoming increasingly involved with drugs. Homicides are spiraling upward, and prison rates and teen pregnancies are rising. If the city is to move ahead, it must turn around this situation with its youth. The potential exists for the District to step into a new era, but it can't fulfill that potential with half its younger generation self-destructing.

The numerous young people involved in this election as candidates and key campaign aides are a magnificent ray of hope. In her victory speech, Dixon heaped lavish praise on her young campaign workers, especially campaign manager David Byrd, 29. Donna Brazille, 30, helped steer Norton's often rocky campaign.

The District boasts a lot of talent. I believe the collective wisdom of all ages and segments of this city, working with the newly elected leadership, can bring the positive and negative lessons from the past to bear on today's problems and use those lessons to step into an outstanding future.