* World stocks up, recover early losses
* Wall Street set for positive open
* European stocks flat, Japan up 0.3 percent
* Dollar falls, reverses earlier gains
By Jeremy Gaunt, European Investment Correspondent
LONDON, June 2 (Reuters) - World stocks edged higher on Tuesday, shrugging off earlier weakness and adding to a buoyant session a day ago.
The dollar also reversed direction and fell again against a basket of major currencies.
MSCI's all-country world stock index was up 0.2 percent, close to the new 2009 high it reached on Monday.
European shares were flat. The FTSEurofirst 300 index of top European shares closed at its highest level in five months on Monday.
Japan's Nikkei stock average closed up 0.3 percent, the second straight day it has ended at 8-month highs.
Investors have been lifted recently by signs that the global economy is on the mend. The latest came from Australia on Tuesday, which had better-than-expected net exports and a rise in monthly new home approvals.
Euro zone April unemployment, however, hit a new 10-year high and the Swiss economy posted its worst quarter in decades.
"Economic indicators are now showing improvement from the worst period but until we see proof of a recovery in company results, it'll be difficult for the market to rise strongly and we're still a long way from the next earnings period," said Takashi Ushio, head of investment strategy at Marusan Securities.
DOLLAR SLIDES
The dollar slipped again. On Monday, it hit its lowest this year versus a basket of currencies.
"Signs of improvement in the economy as well as improving financial conditions continue to weigh on the dollar," said Lee Hardman, currency economist at Bank of Tokyo-Mitsubishi UFJ.
The dollar index was down 0.4 percent at 78.854 after hitting its lowest since mid-December at 78.586 the previous day.
The euro was up 0.4 percent at $1.4214, having rallied to $1.4246 on trading platform EBS on Monday, its strongest since late December.
On euro zone bond markets, the 10-year Bund yielded 3.666 percent, down 3 basis point while the two-year Schatz yield was at 1.425 percent. (Additional reporting by Tamawa Desai, editing by Mike Peacock) (To read Reuters Global Investing Blog click on http://blogs.reuters.com/globalinvesting; for the MacroScope Blog click on http://blogs.reuters.com/macroscope; for Hedge Fund Hub click on http://blogs.reuters.com/hedgehub)