A specific relationship must be met in case of: (a) a structural unit derived from propylene is present in 100 to 85 mole %, and a structural unit derived from ethylene and/or alpha-olefin with 4 to 20 carbons is present in 0 to 15 mole %; (b) a content of a position irregularity unit based on 2,1-insertion of a propylene monomer unit in all propylene insertions, which is measured by 13C-NMR, is 0.5% to 2.0% and a content of a position irregularity unit based on 1,3-insertion of propylene monomer unit in all propylene insertions, which is measured by 13C-NMR, is 0.005% to 0.4%; and (c) a water vapor transmission rate is Y [9/M.sup.2/24 hr] as film and a melting point Tm[.degree. C.] shows specific relationship.