Geodesic
Young measures as measurable functions and applications to variational problems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 191-212

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It is given a systematic approach to the theory of Young measures based on the characterisation of these objects as measurable functions with values of a compact metric space with metric having an integral form. The advantages of this approach to the investigation of the behaviour of integral functionals on weakly convergin sequences are explained. 
@article{ZNSL_2004_310_a9,
     author = {M. A. Sychev},
     title = {Young measures as measurable functions and applications to variational problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {191--212},
     publisher = {mathdoc},
     volume = {310},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a9/}
}
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M. A. Sychev. Young measures as measurable functions and applications to variational problems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 191-212. http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a9/