Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the closed graph...

closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem states...

Borel spaces and f : X → Y {\displaystyle f:X\to Y} then f {\displaystyle f} is measurable if and only if the graph of f {\displaystyle f} is Borel....

also contributed to refinement of the law, including Chebyshev, Markov, Borel, Cantelli, Kolmogorov and Khinchin. Markov showed that the law can apply...

as the De Bruijn–Erdős theorem stating that every minimal k-chromatic graph is finite, and the Curtis–Hedlund–Lyndon theorem providing a topological...

Ax–Grothendieck theorem (model theory) Barwise compactness theorem (mathematical logic) Borel determinacy theorem (set theory) Büchi-Elgot-Trakhtenbrot theorem (mathematical...

fixed-point theorem Banach fixed-point theorem Bekić's theorem Borel fixed-point theorem Bourbaki–Witt theorem Browder fixed-point theorem Brouwer fixed-point...

In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic...

Lusin's separation theorem (descriptive set theory) states that for any two disjoint analytic subsets of a Polish space there is a Borel subset containing...

random graph is unchanged by a relabeling of its vertices: that is, the labels of the vertices carry no information. There is a representation theorem for...

bijective or surjective. The theorem has several "real world" illustrations. Here are some examples. Take two sheets of graph paper of equal size with coordinate...

Ryll-Nardzewski measurable selection theorem says that if X is a Polish space and B {\displaystyle {\mathcal {B}}} its Borel σ-algebra, C l ( X ) {\displaystyle...

Lebesgue–Vitali theorem Blaschke–Lebesgue theorem Borel–Lebesgue theorem Fatou–Lebesgue theorem Riemann–Lebesgue lemma Walsh–Lebesgue theorem Dominated convergence...

then any Borel homomorphism from G to H is continuous. Secondly, there is a version of the open mapping theorem or the closed graph theorem due to Kuratowski:...

(Avraham Trahtman, 2007) Robertson–Seymour theorem (Neil Robertson, Paul Seymour, 2004) Strong perfect graph conjecture (Maria Chudnovsky, Neil Robertson...

of orientable surfaces Planar graph: genus 0 Toroidal graph: genus 1 Teapot: Double Toroidal graph: genus 2 Pretzel graph: genus 3 The non-orientable genus...

{\displaystyle F\in BV} defines a Radon measure (i.e. a locally finite Borel measure on R {\displaystyle \mathbb {R} } ), this definition can be extended...

theorem Goodstein's theorem Green's theorem (to do) Green's theorem when D is a simple region Heine–Borel theorem Intermediate value theorem Itô's lemma Kőnig's...

covolume. The terminology introduced above is coherent with this, as a theorem due to Borel and Harish-Chandra states that an arithmetic subgroup in a semisimple...

commonly written as ln(x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among...

X\times Y} is a countable Borel relation. If f : X → Y {\displaystyle f:X\to Y} is a function between standard Borel spaces, the graph Γ ( f ) {\displaystyle...

Blaschke–Lebesgue theorem Chaplygin problem: isoperimetric problem is a zero wind speed case of Chaplygin problem Curve-shortening flow Expander graph Gaussian...

class is the natural number n. Borel equivalence relation Cluster graph – Graph made from disjoint union of complete graphs Conjugacy class – In group theory...

functions not of exponential type. Nachbin's theorem gives necessary and sufficient conditions for the Borel transform to be well defined. Since an ordinary...

curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence of...

any free group G may be realized as the fundamental group of a graph X. The main theorem on covering spaces tells us that every subgroup H of G is the...

is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics...

variable can be regarded, in the simplest case, as the area between the graph of that function and the X axis. The Lebesgue integral, named after French...

hypercubes get divided by every midplane), as in the proof of the Heine–Borel theorem. A finite subdivision rule R {\displaystyle R} consists of the following...

polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing Polyhedral graphs Random geometric graphs Voronoi diagrams...