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[en] We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm)4 to (7.3 fm)4. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator Dren(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found the Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior ∼(p2+mg2)-1 for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm)4 - we estimate a corresponding infrared (mass) scale to be mIR∼0.7 GeV.