Tacchi, Matteo, et al. "Exploiting Sparsity for Semi-Algebraic Set Volume Computation." arXiv preprint arXiv:1902.02976 (2019). https://arxiv.org/pdf/1902.02976.pdf
Korda, Milan, and Didier Henrion. "Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets." Optimization Letters 12.3 (2018): 435-442. https://arxiv.org/pdf/1612.04146.pdf
Particularly useful references:
Henrion, Didier, Jean B. Lasserre, and Carlo Savorgnan. "Approximate volume and integration for basic semialgebraic sets." SIAM review 51.4 (2009): 722-743. https://pdfs.semanticscholar.org/893b/e70a990901d7b6b2f052cbcb5883a043b5d9.pdf
Tacchi, Matteo, et al. "Exploiting Sparsity for Semi-Algebraic Set Volume Computation." arXiv preprint arXiv:1902.02976 (2019). https://arxiv.org/pdf/1902.02976.pdf
Korda, Milan, and Didier Henrion. "Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets." Optimization Letters 12.3 (2018): 435-442. https://arxiv.org/pdf/1612.04146.pdf
Somewhat related references: