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Let $ \gamma$ be a limit ordinal with cofinality $ \kappa > \omega$ . Is there a stationary subset of $ \gamma$ (a subset of $ \gamma$ that meets every closed unbounded subset of $ \gamma$ ) of size $ \kappa$ ?Read more

Let $ \lambda\geq \omega_2$ be a regular cardinal and $ S\subset[\lambda]^\omega$ be a stationary set. I’m looking for a property of $ S$ , say “shootable”, such that there exists a forcing extension preserving $ \lambda, \omega_1$ as cardinals that shoots a club into $ S$ . I’ve encountered ad hoc examples, but I’d reallyRead more

i have proof question that i cant seem to understand why it is true, it goes like this: For a finite ergodic markov chain Xn with J states (1,2,..,J) and transition matrix P. show that if we find vector (X1,X2,..,XJ) such that SUM(Xi)=1 and XiPij=XjPji for every i,j then (X1,X2,..,XJ) is the stationary distribution. now,Read more

Let $ \phi(\mathbf{x}; A_1, \ldots, A_n)$ where $ a_i \leq A_i \leq b_i$ and $ \phi(\mathbf{x}; A_1, \ldots, A_n)$ is a smooth real function for each choice of $ A_i$ ‘s. Let us fix a smooth function $ \psi(\mathbf{x})$ , which supp $ \psi$ is contained in a compact set $ K$ . Suppose IRead more

(1) With matrics $ {\bf{A}},{\bf{B}}$ and $ {\bf{C}}$ , how can I represent $ {\bf{M}}{\rm{ = }}\left( {\begin{array}{*{20}c} {a_{11} {\bf{B}}} & {a_{12} {\bf{B}}} \ {a_{21} {\bf{C}}} & {a_{22} {\bf{C}}} \ \end{array}} \right)$ by using $ {\bf{A}},{\bf{B}}$ and $ {\bf{C}}$ ? (2) If $ {\bf{M}}{\rm{ = }}\left( {\begin{array}{*{20}c} {a_{11} {\bf{B}}} & {a_{12} {\bf{B}}} \ {a_{21} {\bf{B}}}Read more

I already asked this question in StackExchange, but found little attention. So I’m just going to copy-paste my original question here. Let $ P$ be a stochastic matrix (of an irreducible Markov Chain) with stationary distribution $ \pi^T$ (i.e. $ \pi^T P = \pi^T$ ) and let further $ E$ be the matrix of allRead more