Jackson-type theorem in the weak $L_{1}$-space

The weak $L_{1}$-space meets in many areas of mathematics. For example, the conjugate functions Lebesgue integrable belong to $L_{1}$-space. difficulty working with is that not a normed space. Moreover, infinitely differentiable (even continuous) are dense this Due this, theory approximation was produced In present paper, we introduced concept modulus continuity from $L_{1}$-space, studied its properties, found criterion for convergence zero function and proved space an analogue Jackson-type theorem.