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What this would mean is that the economy was experiencing deflation.
Deflation is when the price level for the economy as a whole drops. If the price level is dropping, a small increase in production in the economy as a whole could still result in a decline in nominal GDP because the decline in price would offset the increase in production.
In such a case, real GDP would rise because production was rising but nominal GDP would drop because the price (in current dollars) of the goods and products made would be lower due to the deflation.
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