Updated from 6:56 a.m.

NEW YORK (TheStreet) -- Here are 10 things you should know for Tuesday, June 2:

1. -- U.S. stock futures were trending downward as investors prepared for more economic data Tuesday.

European stocks declined Tuesday on Greek debt worries, even as better-than-expected eurozone consumer price data suggested a government bond-buying program by the bloc's central bank has chased away the specter of a prolonged period of Japanese-style deflation.

Falling prices of commodities weighed on Asian stocks, though mainland Chinese indices continued their recovery on hopes for further economic and monetary stimuli from Beijing. The Shanghai Composite index closed up, and in Hong Kong, the Hang Seng fell. In Tokyo, the Nikkei 225 sank slightly, as did the Topix.

2. -- The economic calendar in the U.S. on Tuesday includes the Gallup Economic Confidence Index at 8:30 a.m., the comparable-store sales Redbook at 8:55 a.m., and factory orders data at 10 a.m. Motor vehicle sales data will also be reported Tuesday.

3. -- U.S. stocks on Monday rose modestly on positive economic data to kick off June.

The Dow Jones Industrial Average (DIA) rose 0.18% to 18,040.37. The S&P 500 (SPY) closed up 0.21% to 2,111.73. The Nasdaq (QQQ) increased 0.25% to 5,082.93.

4. -- In its quest to refinance its debt and stabilize its national financial situation, Greece has offered to reform its pensions, according to reports. The new governing party, Syriza, was elected on a platform that opposed austerity, so the move is somewhat unexpected.

Without serious reforms, however, Greece is looking at a default on its debt -- it owes a payment of €300 million ($330 million) to the International Monetary Fund on Friday, and much bigger payments eventually -- as well as bankruptcy and a potential exit from the eurozone.

5. -- More details about Intel's (INTC) $16.7 billion deal to buy Altera (ALTR) are unfurling. The deal, announced Monday, will allow Intel to acquire Altera's data-center microchip business, as well as the programmable chips Altera designs to boost Web traffic speeds.

The semiconductor industry has been contracting, and this is one of several recent deals in the field. The personal computer market appears to be contracting, and chipmakers are looking for any advantage in the market.

In premarket trading, Intel stock was sinking by 0.34% after closing down 1.6% Monday. Altera stock was dropping by 0.15% after Monday's 5.8% jump.

6. -- Gas prices may have already hit their high point for the year, according to car advocacy group AAA. The group said that crude oil costs were stabilizing and that the month of June usually shows gas price drops.

Gas prices are up 71 cents for the year on average. Still, OPEC predicted that oil prices would remain low through 2017.

7. -- Generic drugmaker Mylan (MYLdemanded an explanation from Teva Pharmaceuticals (TEVA) about Teva's acquisition plans for Mylan. Teva offered to buy Mylan for $40 billion in April, but Mylan's leaders seemed skeptical of Teva's plan.

In premarket trading, Mylan stock was falling by 0.78%. Teva's ADRs were level.

8. -- ISM Manufacturing data showed that the manufacturing sector was expanding. The economy has grown for 72 months in a row, according to the report.

The manufacturing report suggests the economy is stronger than it might seem to be. "This was a very strong ISM manufacturing sector report, and it comes at a time when doubts about the rebound in economic growth momentum are beginning to surface," said Millan Mulraine, U.S. strategist at TD Securities, to TheStreet's Keris Alison Lahiff. "For the [Federal Reserve], this report should do little to change the dynamics at the next meeting later this month, and we continue to see September as the earliest possible time for the Fed to get the necessary confirmation in the recovery to justify raising rates."

9. -- Health insurance premiums look to be heading upward for next year, although they vary considerably. The federal government reported that some insurers would raise rates by 85% in 2016. The data comes from the federal HealthCare.gov Web site, which governs the 37 states that lack individual health cae exchanges.

10. -- The earnings calendar on Tuesday includes Dollar General  (DG) before the market open and Ambarella (AMBA) after the market close.

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