On some embedding theorems for ideal structures

The appearance of the first embedding theorems, as well as the term “embedding” itself, is associated with the name of Academician S. L. Sobolev. The further development of the theory of embedding of spaces proceeded in two directions: 1) embedding theorems for differentiable functions; 2) embedding theorems for spaces of measurable functions. The authors obtained embedding theorems for symmetric and more general ideal spaces of measurable, in the sense of Lebesgue, functions.