NEW YORK, MARCH 2 -- The stock market wound up clinging to a small gain today after a broad early advance faded.

The Dow Jones average of 30 industrials, up about 15 points at its best level of the day, finished with a 0.83 point rise at 2071.29.

Advancing issues outnumbered declines by about 5 to 3 on the New York Stock Exchange.

Big Board volume totaled 199.63 million shares, down from 199.99 million in the previous session. The NYSE's composite index rose .50 to 150.68. The Dow industrials have essentially gone nowhere in the past two days after jumping 48 points Monday. But as has been the case for the past couple of months, broader market measures were generally strong today, reflecting continuing interest in many depressed secondary issues.

Analysts said the market was still benefiting from growing confidence that a recession can be avoided despite the market's collapse last autumn.

One theoretical warning of a business slump was lifted Tuesday, when the Commerce Department issued new figures on its index of leading economic indicators. With an upward revision of the December figure for the index from a decline to a gain, it no longer showed a string of three consecutive lower readings.

But with all that, they said, many investors still seemed leery of chasing after an advance that has carried the market to its highest levels since the collapse.

J.P. Stevens rose 1 7/8 to 56 3/8. West Point-Pepperell made a bid of $56 a share for the company Tuesday, in competition with a management-led group that is seeking to buy it out.

Xerox gained 2 3/4 to 61 3/4 amid a variety of rumors. The company said it had no explanation for the unusual activity in its stock.

Japanese issues moved up following a strong day in the Tokyo market. Kubota Ltd. rose 7 to 99 1/2; Matsushita 4 5/8 to 187 1/8, and Honda Motor 3 1/4 to 122.