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For a very good reference see Eckland and Turnbull, Infinite-Dimensional Optimization and Convexity.

Much of the literature on measure theory in linear spaces focuses on the case of normed linear spaces (e.g., the outstanding book by Vakhania, or its sequel). However, nuclear linear spaces "as far fr …

In applications, Hilbert spaces of interest are often assumed to be separable. In addition to being extremely convenient mathematically, this assumption can often be justified on computational or phys …

Motivation: Let $\Gamma = (V,E)$ be a directed graph. To each edge $e \in E$, choose a value $\kappa^e \in \mathbb R$, representing the cost of transporting one unit of "stuff" through the edge. Let $ …

Let $Q$ be a locally compact Hausdorff space, and let $V$ be a topological vector space. Consider the space $X = C_0(Q, V)$ of $V$-valued fields which vanish at infinity. Let $X^*$ denote the dual spa …

MathOverflow itself serves as an excellent reference tool for this sort of triangulation. When a future researcher googles the topic of lextensive categories with strongly orthogonal orbits (perhaps w …

This is just a nomenclature question. Let $T$ be a commutative monoid, and let $T^*$ be its Grothendieck group. That is, $T^* \cong T \times T \ / \sim$, where $(s,s') \sim (t, t')$ if $s+t'+e = s'+t+ …

In another thread, I asked about the $M$ endofunctor on the category $\operatorname{Meas}$ of measurable spaces, which sends a space $X$ to its space of measures $M(X)$. Will Sawin described the mon …

Let $d \ge 1$, and consider the integer lattice $\mathbb Z^d$. This is a homogeneous space, in the manner of the Erlangan Programm. I would like to write $\mathbb Z^d = G / H$, where $G$ is the symm …

Let $M$ be a differentiable manifold, let $TM$ be its tangent bundle, and consider $TTM$, the double tangent bundle. Let $V \subseteq TTM$ denote the vertical subbundle, which is determined in a cano …

I am working with a class of matrices $A$ which are non-negative-definite, not symmetric, and have maximum eigenvalue less than 1. I am interested in the spectral properties of the matrix $H = A(I - …

This is an answer to your question, What general resources exist for students in highschool who are very interested in Mathematics? A patient teacher is the best resource for an interested high …

In addition to the excellent answers above, I also suggest the nice survey Oxtoby, Ergodic Sets (Zbl 0046.11504, MR47262, DOI: 10.1090/S0002-9904-1952-09580-X). Introduction. Ergodic sets were introd …

Let $X$ and $Y$ be Poisson random variables with means $\lambda$ and $1$, respectively. The difference of $X$ and $Y$ is a Skellam random variable, with probability density function $$\mathbb P(X - Y …

The following question came up in a discussion with my advisor: Let $(\Omega, \mathcal F, \mathbb P)$ be a non-trivial probability space, and suppose that $\mathcal G$ is a proper sub-$\sigma$-alg …