The Supreme Court yesterday let stand a ruling that the Miller Brewing Co. may not appropriate the words "lite" or "light" for exclusive use as a trade mark name for its low-calorie beer.

The justices rejected Miller's request that it review a U.S. Appeals Court ruling that "light" is a common descriptive word and neither it "nor its phonetic equivalent may be appropriated as a trademark for beer."

The high courts's action does not set any national legal precedent, but does settle the law in the seventh Federal Judicial Circuit covering Indiana, Illinois and Wisconsin, where Miller is suing three companies for trademark infringement.

Miller had hoped to reverse an appeals court decision involving G. Heileman Brewing Co.

Other brewers named by Miller in infringement suits are Schlitz, Genesee, Peter Hand, Antheuser-Busch, Pittsburgh Brewing, Erie Brewing, Olympia, Rheingeld and Rainier. Phone Regulation

The Supreme Court also let stand a decision requiring the established telephone system in California to allow a Los Angeles-San Diego tie-in of a private carrier, southern Pacific Communications Co.

The connection with Pacific Telephone and Telegraph Corp. would allow further connection with American Airlines' nationwide private system.

The 9th U.S. Circuit Court of Appeals had upheld a decision by the Federal Communications Commission to require the link. California and the National Association of Regulatory Utility Commissioners had claimed that the problem was an intrastate matter for decision by a state agency alone.

Southern Pacific - orginally an inter state service between San Francisco, Los Angeles, Phoenix and Tucson - had obtained limited permission from the California Public Utilities Commission to transmit voice and data by private line between Bakersfield, Fresno, Los Angeles, Merced, San Francisco and Stockton.

The state commission attempted to minimize rate competition with Pacific Telephone and forbade certain connections such as "foreign exchange," which provides a dial tone for a customer many miles from the city he is calling.

Southern Pacific's move to obtain a connection of this kind with PT&T brought the jurisdictional issue to the federal agency. Vesco Ruling

For the third time in less than four years, the Supreme Court refused to hear arguments by a company controlled by fugitive financier Robert L. Vesco.

The court led stand a decision by the 2nd U.S. Circuit Court of Appeals that Vesco & Co., Inc., must pay the money a federal court ruled Vesco owes to the International Controls Corp. UMW Pensions

The court also let stand a lower court's ruling that could cost the United Mine Workers union $10 million in pension contributions to the Anthracite Health and Welfare Fund.

The justices refused to review a decision handed down last April by the 3d U.S. Circuit Court of Appeals that four miners receiving benefits under the financially shaky retirement fund had a right to sue their union.

Four Pennsylvania pensioners first sued the UMW in 1963, a year after the fund treasury was owed $12 million in delinquent payments from coal operators.

Their suit charged that the union and fund trustees favored the interests of working miners over those of retired miners, and therefore failed to make sure delinquent payments from coal operators were collected. Lipper Corp. Case

The Supreme Court refused to hear an appeal by the federal government contending that the Arthur Lipper Corp. and its president, Arthur Lipper III, should be barred permanently from the securities business.

At the same time, the justices truned down an appeal from Lipper contending that a one-year suspension was unjustified.