Divergent mass integrals and problem of the factor 4/3 in the classical electrodynamics

Inconsistency of different definitions of the electromagnetic mass of the classical electron is treated. It is shown that the values of the divergent integrals, in terms of which the energy and momentum of a point charge are expressed, depend upon the choice of the frame. Therefore, formal comparison of the quantities expressed in terms of these integrals turns out to be random and depends on the method used to calculate the integrals. Improper integrals which are logarithmically divergent are an exclusion. It is shown that introduction of the vacuum dielectric constant, which depends on field vectors and leads to elimination of divergencies in the electron energy and momentum integrals, simultaneously removes the 4/3 problem in the theory of classical electron