Approximate Conditions and Passage to the Limit in Sobolev Spaces over Thin and Composite Structures

Approximate properties of variable measures compose a base of the two-scale convergence method with respect to a variable measure, which is used in averaging on periodic thin and composite structures. The paper gives a survey of methods for verifying approximate properties. The main focus is on studying composite measures, which have been little studied. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial Differential Equations, 2004.