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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

2 votes

Extending the product measure on $2^\omega$

There is no such measure. Suppose toward contradiction $\mu$ is such a measure. Partition $\Omega$ by the mod finite equivalence relation $\sim_{\text{fin}},$ let $X \subset \Omega$ be a choice of rep …
Elliot Glazer's user avatar
4 votes
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Is there a maximal translation-invariant extension of Lebesgue measure?

The answer is no. This is the main result of "Extensions of invariant measures on Euclidean spaces" by Ciesielski and Pelc.
Elliot Glazer's user avatar