This Letter reports results from the NEMO-3 experiment based on an exposure of 1275 days with 661g of 130Te in the form of enriched and natural tellurium foils. The double beta decay rate of 130Te is found to be greater than zero with a significance
of 7.7 standard deviations and the half-life is measured to be T1/2 = (7.0 +/- 0.9(stat) +/- 1.1(syst)) x 10^{20} yr. This represents the most precise measurement of this half-life yet published and the first real-time observation of this decay.
In the double beta decay experiment NEMO~3 a precise knowledge of the background in the signal region is of outstanding importance. This article presents the methods used in NEMO~3 to evaluate the backgrounds resulting from most if not all possible o
rigins. It also illustrates the power of the combined tracking-calorimetry technique used in the experiment.
