THE RECENTLY concluded presidential campaign of California's Gov. Edmund G. Brown Jr. ratified by its failure an ancient and honored political maxim: "all business is local."

What Gov. Brown learned in 1980, at the cost of a lot of money and some embarrassment, is that Democratic primary voters, outside of California, knew and cared about what Mr. Brown had been doing in California, between presidential campaigns. Jerry Brown had been the 1976 political Rookie of the Year on the strength of late primary victories over Jimmy Carter in Maryland, Rhode Island, New Jersey, Nevada and California. That year, Mr. Brown was able to forge an eclectic coalition of party regulars, parts of organized labor, environmentalists and younger voters in his string of victories.

In winning reelection as governor in 1978, Mr. Brown had to negotiate California's budget-cutting Proposition 13. He began by calling the initiative "a consumer fraud" and "a rip-off," and ended by embracing the proposal so completely that one skeptic called Mr. Brown "the Stepfather of Proposition 13."

Mr. Brown's conversion to fiscal austerity was demonstrated by his 1979 public advocacy of a balanced-budget constitutional amendment -- and a constitutional convention to achieve it. Constitutional amendments invariably send shivers through the hearts of liberal Democrats, and the mere mention of a constitutional convention can cause cardiac arrest in the same constituency. Mr. Brown later dropped the convention proposal from his campaign message, but the damage had already been done. As his detractors had been insisting, in the eyes of many voters Jerry Brown was either an opportunist or a "flake," or both.

The Brown candidacy was probably doomed on the day that Sen. Edward Kennedy entered the race against President Carter and the contest was widely perceived as a two-man contest. In Iowa, Gov. Brown went so far as to enter an unsolicated and unsuccessful coalition with Uncommitted, to the benefit of neither in the caucuses.

The irony is that, if anything, the message of Gov. Brown -- austerity, era of limits and alternative energy development -- seemingly would have had greater appeal this campaign year than in 1976. But the failure of the 1980 Brown campaign can probably be attributed to the voters' negative verdict on the messenger by the reports that a number of people are urging Rep. John Anderson to run as a third-party candidate in November, and no one is publicly urging such a course on Gov. Brown. Maybe John Anderson is the real Jerry Brown of 1980.