The effective complex conductivity σ* of an n‐component composite material is considered. Recently, an integral representation that treats the component conductivities σ1,...,σn symmetrically was developed. This representation has the advantage that the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. However, the admissible class of measures has been difficult to characterize, due to the condition that σ* is a homogeneous function of the component conductivities. Here, this admissible class is characterized in terms of linear relations among the moments associated with tetrahedra in Fourier space Zn. The homogeneity is used to derive a new formula for σ* in the two‐component case, in which σ* for general media is expressed in terms of the conductivities of laminates of second rank.

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