For the devoted, borderline-demented sports nut, it is Christmas here every day.

What government is to Washington, business to New York, culture to Boston, gambling to Las Vegas and foreclosure to Cleveland, that 's what big-time sports is to Los Angeles.

It is the ocnstant backdrop, the perpetual accompaniment of all other activities.

In this community that has made an industry out of stargazing, it is the movie and music supernovas who come to the jocks for approval.

Here, Frank Sinatra comes to Tom Lasorda's opening night, Jack Nicholson whistles and stomps in the front row for Kareem Abdul-Jabbar, and Johnny Carson Iaments on nation-wide television about the Rams.

Tinseltown is fascinated by real sweat. Perhaps only in Hollywood and Beverly Hills could a sporting event's final score seem to be an undeniable and permanent proof of excellence.

This is the only American city where a local team being involved in a World Series, aRose Bowl, or an NFL playoff game barely seems to make a ripple. It's the norm.

Only stadium-littered L. A. could offer to host the 1980 Olympics without needing to build any huge new facilities. And only L. A. would think of asking by referendum, "Hey, who needs the Olympics? Do we really want the bother? Can it pay its own way?"

It is taken for granted here that L. A. is the hub of the athletic universe and that its weekly succession of ultimate, classic, cliche-filled confrontations will continue indefinitely-world without end zone, amen.

We're not talking about racketball for fatties or Frisbee golf. Klutzes ye shall always have with you. Why, just down the coast highway in San Diego you have a burg that calls itself "Sportstown, U.S.A.," because its avowed civil aspiration is to have a blister on every San Diegan toe.

Phooey! Mankind can jog anywhere-even in L. A., it is said, if you wear a gas mask.

No, we are talking about serious sports business, and the best place for that is right here.

Nothing in the realm of American sports has escaped Los Angeles. It has one of everything and two of most. And what it has is usually the richest, most pampered, and best.

What truly differentiates Los Angeles is the number and quality of its events and the beauty of it sSouthern California venues.Nevertheless, the addicted all-sports fan might think he was in video heaven if he never left a hotel room.

On this Christmas weekend, the Sun Bowl, Peach Bowl and an NFL playoff all kicked off on the L. A. tube by 10 a.m. The continuous feast of games did not end until the Tangerine Bowl and UCLA basketball game ended late at night. Viva la time difference, say the jock junkies, who savor the extra hours of morning viewing.

After a good night's sleep, you can wake up, flip on the tube and watch Brent, Irv, Jayne and the Greek on "The NFL Today" at 8.30 a.m. if you can swallow them on an empty stomach.

Other towns sometimes blush when their games become gargantuan; Los Angeles never does. This is the city that calls its 100,000-seat ballpark. The Coliseum and one of its gyms The Forum.

If the Caesars had bread and circuses, then Angelenos can have tacos and touchdowns. And they have them in huge quantities.

In some cities, attending a great variety of sports events is more likely to be seen as adolescent than chic. Even in a sports-mad town like Boston it is usually one or two traditional teams to which a sane person admits being addicted, like confessing some quaint inherited family affliction.

However, in L. A., going to "The Game sport it is) is considered the socially "in" thing to do. Perhaps the Hollywood stars in those conspicuous seats lend a sort of community seal of approval.

Also, there is a kind of regional Southern California pride in making use of the perpetual sunshine.

In this environment, both social and climatic, every sport flourishes, not just a few pro favorites.

In fact, New York has more pro teams than L. A., 7 to 5, although the Dodgers, Angels, Lakers, Kings and Rams have an overall edge in quality.

More important, the home stadiums of L. A. teams probably are the most pleasing in any American city.

No baseball park has an alpine mural behind it like the San Gabriel mountains standing behind the Dodgers' playground in Chavez Ravine. That scenery and airy Spanish architecture are two nonbaseball reasons why Dodger Stadium drew a record 3.2 million this year.

The Big A, home of the baseball Angels, down the Santa Ana freeway in Anaheim, has a hint of adjoining Disneyland contaminating it but that can be forgiven.

The Forum, in Inglewood, home of the NBA Lakers and NHL Kings, resembles a circular marble Parthenon. Just looking at their majestic home ought to make the Lakers hustle. But it never does.

L. A.'s greatest sports charm is its diversity. No city can offer a crosstown college rivalry between tow basketball and football empires like USC and UCLA. Pauley Pavilion in lovely manicured Westwood is the Boston Garden of college basketball-the home of unmatched champions.

The USC-UCLA connection also makes the Rose Bowl seem a private joust between the Los Angeles city football champions and latest collection of dinosaurs from the Big Ten.

From the air, Los Angeles resembles a huge playground dotted everywhere with football and baseball fields, golf courses, tennis courts and enough swimming pools to backstroke from Santa Monica to Orange County.

It's hard to believe that the West was settled by people who believed in work.

The sports year in this setting abides by no seasons. L. A. has a calendar with 12 Julys. "What do you open the day after Christmas?" asks the favorite holiday radio jingle here. "That's right (ringing of bells, opening of starting gates).Santa Anita!"

In this megalopolis where downtown Santas wear Bermuda shorts, why shouldn't gorgeous Santa Anita, with its sculptured gardens and waterfall, open on Dec. 26?

Racing is just another L. A. passion, from Hollywood Park and Los Alamidos tracks for horses, to Riverside and Ontario speedways that accommodate a dozen different auto races a year.

Naturally, there is a Greater Los Angeles Open for pro golf, and the tennis Davis Cup came to no-so-far-away Palm Springs.

In fact, is there a sport so moribund that it cannot make a buck in L. A.? It doesn't seem so. Even boxing flourishes here at the Olympia, and the Los Angeles Oranges of World Team Tennis actually show a profit.

Those who fear that sport will, by the end of the century, saturate and overexpose itself, need only look at Los Angeles to see a glimpse of the future. Traces of the blase blues are visible here. Dodger World Series crowds seemed distant and hard to please, more like folks at the opening of a new movie than rabid delighted fans.

"Okay, show me what you got," says the omnivorous L. A. fan. "Make me have a good time." Contenders who never quite gain a crown, much as the Rams and the Lakers, are castigated. Just winning isn't enough.

Nevertheless, most of the evidence in hand is that, in L. A., the sports boom feeds on itself.

Surely no other town has ever been offered such a banquet of sports. Yet the insatiable Angeleno merely gives a polite burp and asks, "What's for dessert?"