Axon, Logan M., Algorithmically random closed sets and probability, Ph.D Thesis, ProQuest LLC, University of Notre Dame, Ann Arbor, MI, 2010.
Barmpalias, George, Brodhead, Paul, Cenzer, Douglas, Dashti, Seyyed, and Weber, Rebecca, Algorithmic randomness of closed sets. Journal of Logic and Computation, vol. 17 (2007), no. 6, pp. 1041–1062.
Brodhead, Paul, Computable aspects of closed sets, Ph.D Thesis, ProQuest LLC, University of Florida, Ann Arbor, MI, 2008.
Brodhead, Paul, Cenzer, Douglas, Toska, Ferit, and Wyman, Sebastian, Algorithmic randomness and capacity of closed sets. Logical Methods in Computer Science, vol. 7 (2011), no. 3:16, Special issue: 7th International Conference on Computability and Complexity in Analysis (CCA 2010).
Choquet, Gustave, Theory of capacities. Annales de l’Institut Fourier, Grenoble, vol. 5 (1953–1955), pp. 131–295.
Mauldin, R. Daniel and McLinden, Alexander P., Random closed sets viewed as random recursions. Archive for Mathematical Logic, vol. 48 (2009), no. 3–4, pp. 257–263.
Day, Adam R. and Miller, Joseph S., Randomness for non-computable measures. Transactions of the American Mathematical Society, vol. 365 (2013), pp. 3575–3591.
Diamondstone, David and Kjos-Hanssen, Bjørn, Members of random closed sets, Mathematical theory and computational practice, Lecture Notes in Computer Science, vol. 5635, Springer, Berlin, 2009, pp. 144–153.
Downey, Rod, Hirschfeldt, Denis R., Nies, André, and Terwijn, Sebastiaan A., Calibrating randomness. Bulletin of Symbolic Logic, vol. 12 (2006), no. 3, pp. 411–491.
Fouché, Willem, Arithmetical representations of Brownian motion. I, this Journal, vol. 65 (2000), no. 1, pp. 421–442.
Fouché, Willem, The descriptive complexity of Brownian motion. Advances in Mathematics, vol. 155 (2000), no. 2, pp. 317–343.
Hertling, Peter and Weihrauch, Klaus, Random elements in effective topological spaces with measure. Information and Computation, vol. 181 (2003), no. 1, pp. 32–56.
Kjos-Hanssen, Bjørn, The probability distribution as a computational resource for randomness testing. Journal of Logic and Analysis, vol. 2 (2010), p. 10, .
Kjos-Hanssen, Bjørn and Nerode, Anil, The law of the iterated logarithm for algorithmically random Brownian motion, Logical foundations of computer science, Lecture Notes in Computer Science, vol. 4514, Springer, Berlin, 2007, pp. 310–317.
Matheron, G., Random sets and integral geometry, Wiley Series in Probability and Mathematical Statistics, Wiley, New York–London–Sydney, 1975.
Molchanov, Ilya, Theory of random sets, Probability and its Applications (New York), Springer-Verlag, London, 2005.
Nguyen, Hung T., An introduction to random sets, Chapman & Hall/CRC, Boca Raton, FL, 2006.
Nies, André, Computability and randomness, first ed., Oxford Logic Guides, Oxford University Press, New York, 2009.
Reimann, Jan and Slaman, Theodore A., Measures and their random reals, Transactions of the American Mathematical Society, to appear.