A hydrophobic hollow fiber membrane for membrane distillation, made up of a vinylidene fluoride polymer, wherein the hollow fiber membrane has a wall with a wall thickness, an outer surface on its outside, and an inner surface on its inside facing toward its lumen, - wherein the hollow fiber membrane has a continuous skin on its inner and outer surface, - wherein pores are formed in the skin of the inner surface and in the skin of the outer surface, and - wherein the hollow fiber membrane, adjacent to the skin on the inner surface, has a supporting layer having a microporous, sponge-like, and open-pored structure and having a substantially isotropic pore structure across the wall thickness, said supporting layer extending across at least 80% of the wall thickness and having pores with an average diameter of less than 1 μm, wherein the pore sizes are determined via scanning electron microscopy, characterized in that - the vinylidene fluoride polymer forming the structure of the hollow fiber membrane has a weight average of the molecular weight Mw, determined as in the experimental section of the description, in a range of from 550,000 to 700,000 daltons, and a polydispersity, given by the ratio of the weight average Mw and the numerical average M N of the molecular weight of greater than 3.0, determined as in the experimental section of the description, - the pores in the skin of the outer surface and the pores in the skin of the inner surface have a closed circumference in the plane of the skin, and the pores in the skin of the outer or inner surface have a ratio of their longitudinal extent in the direction of the longitudinal axis of the hollow fiber membrane to their transverse extent in the circumferential direction of the hollow fiber membrane of at most 10, and the pores in the inner skin of the inner surface have a diameter of at most 3 μm, - the pores in the inner surface are smaller than the pores in the outer surface, and the pores in the isotropic region of the supporting layer have a smaller average diameter than the pores in the skin of the outer surface, - the porosity of the hollow fiber membrane, determined as in the experimental section of the description, is in a range of from 50 to 90 vol%, - the wall thickness is in a range of from 50 to 300 μm, and the diameter of the lumen is in a range of from 100 to 500 μm, and - the hollow fiber membrane has a maximum separating pore diameter d max, determined by the bubble point method, in a range of from 0.3 to 0.7 μm. - wherein the hollow fiber membrane has a continuous skin on its inner and outer surface, - wherein pores are formed in the skin of the inner surface and in the skin of the outer surface, and - wherein the hollow fiber membrane, adjacent to the skin on the inner surface, has a supporting layer having a microporous, sponge-like, and open-pored structure and having a substantially isotropic pore structure across the wall thickness, said supporting layer extending across at least 80% of the wall thickness and having pores with an average diameter of less than 1 μm, wherein the pore sizes are determined via scanning electron microscopy, - the vinylidene fluoride polymer forming the structure of the hollow fiber membrane has a weight average of the molecular weight Mw, determined as in the experimental section of the description, in a range of from 550,000 to 700,000 daltons, and a polydispersity, given by the ratio of the weight average Mw and the numerical average M N of the molecular weight of greater than 3.0, determined as in the experimental section of the description, - the pores in the skin of the outer surface and the pores in the skin of the inner surface have a closed circumference in the plane of the skin, and the pores in the skin of the outer or inner surface have a ratio of their longitudinal extent in the direction of the longitudinal axis of the hollow fiber membrane to their transverse extent in the circumferential direction of the hollow fiber membrane of at most 10, and the pores in the inner skin of the inner surface have a diameter of at most 3 μm, - the pores in the inner surface are smaller than the pores in the outer surface, and the pores in the isotropic region of the supporting layer have a smaller average diameter than the pores in the skin of the outer surface, - the porosity of the hollow fiber membrane, determined as in the experimental section of the description, is in a range of from 50 to 90 vol%, - the wall thickness is in a range of from 50 to 300 μm, and the diameter of the lumen is in a range of from 100 to 500 μm, and - the hollow fiber membrane has a maximum separating pore diameter d max, determined by the bubble point method, in a range of from 0.3 to 0.7 μm.