Using data from the NEMO-3 experiment, we have measured the two-neutrino double beta decay ($2 ubetabeta$) half-life of $^{82}$Se as $T_{1/2}^{2 u} = left[ 9.39 pm 0.17,left(mbox{stat}right) pm 0.58,left(mbox{syst}right)right] times 10^{19}$ y under the single-state dominance hypothesis for this nuclear transition. The corresponding nuclear matrix element is $left|M^{2 u}right| = 0.0498 pm 0.0016$. In addition, a search for neutrinoless double beta decay ($0 ubetabeta$) using 0.93 kg of $^{82}$Se observed for a total of 5.25 y has been conducted and no evidence for a signal has been found. The resulting half-life limit of $T_{1/2}^{0 u} > 2.5 times 10^{23} ,mbox{y} ,(90%,mbox{C.L.})$ for the light neutrino exchange mechanism leads to a constraint on the effective Majorana neutrino mass of $langle m_{ u} rangle < left(1.2 - 3.0right) ,mbox{eV}$, where the range reflects $0 ubetabeta$ nuclear matrix element values from different calculations. Furthermore, constraints on lepton number violating parameters for other $0 ubetabeta$ mechanisms, such as right-handed currents, majoron emission and R-parity violating supersymmetry modes have been set.
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