WIAS Preprint No. 2852, (2021)

Precompact probability spaces in applied stochastic homogenization


  • Heida, Martin
    ORCID: 0000-0002-7242-8175

2020 Mathematics Subject Classification

  • 54E45 60D05 74Qxx 76M50 80M40


  • Homogenization, stochastic geometry, precompactness




We provide precompactness and metrizability of the probability space Ω for random measures and random coefficients such as they widely appear in stochastic homogenization and are typically given from data. We show that these properties are enough to implement the convenient two-scale formalism by Zhikov and Piatnitsky (2006). To further demonstrate the benefits of our approach we provide some useful trace and extension operators for Sobolev functions on Ω, which seem not known in literature. On the way we close some minor gaps in the Sobolev theory on Ω which seemingly have not been proven up to date.

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