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This question was previously posted on MSE https://math.stackexchange.com/questions/3305781/estimating-the-measure-of-a-pre-image-of-a-polynomial Let $\sigma := 2/(3\sqrt{3})$, be a real number. And …

This question was previously posted on MSE. Let $f:\mathbb R^3 \to \mathbb R^3$ be a smooth Lipschitz function (bounded if needed), and $W_t$ a $3$-dimentional Brownian motion. Consider the SDE on $\m …

This same question was also posted on MSE https://math.stackexchange.com/questions/3327007/existence-and-uniqueness-of-a-stationary-measure. Recently I have posted the following question on MO Attrac …

This question was previously posted on MSE. This question might be easy but I am really stuck on it. Let $M$ be compact metric space and $\mathcal B(M)$ the Borel $\sigma$-algebra of M. Consider the d …

I believe I found an answer. Note that in a similar way that we constructed $P_\mu,$ we may define $P_x$ as the unique Borel probability on $M^{\mathbb N}$, such that given $A_0,\ldots,A_n \in M,$ the …

Let $X$ be a compact Hausdorff topological space, and $\mathcal C^0 (X) = \{f:X\to\mathbb{R}; \ f \text{ is continuous }\}$. It is well known that for any bounded linear functional $\phi: \mathcal C^ …

Let $\Delta$ be the interval $[-1,1]$, then we can consider the probability space $(\Delta , \mathcal{B}(\Delta),\nu)$, where $\mathcal{B}(\Delta)$ is the Borel $\sigma$-algebra and $\nu$ is equal ha …