Search results for "Carlson's theorem"

showing 4 items of 4 documents

The Second Main Theorem

1998

Pure mathematicsFundamental theoremPicard–Lindelöf theoremCompactness theoremFixed-point theoremBrouwer fixed-point theoremSqueeze theoremMathematicsMean value theoremCarlson's theorem
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Stoïlow’s theorem revisited

2020

Stoilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps z -> z(k) and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed

continuous open and discrete mappingsPure mathematicsContinuous open and light mappingscontinuous open and light mappingsFundamental theoremPicard–Lindelöf theoremGeneral Mathematics010102 general mathematicsRamsey theoryStoilow's theorem16. Peace & justice01 natural sciencesSqueeze theoremfunktioteoriaFactorizationStoilow’s theoremFundamental theorem of calculusContinuous open and discrete mappings111 Mathematics0101 mathematicsBrouwer fixed-point theoremMathematicsCarlson's theoremExpositiones Mathematicae
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Characteristic Functions and the Central Limit Theorem

2020

The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.37) and for independent arrays of random variables (Lindeberg–Feller theorem, Theorem 15.43). For the latter, we prove only that one of the two implications (Lindeberg’s theorem) that is of interest in the applications.

Statistics::TheoryFactor theoremPure mathematicsArzelà–Ascoli theoremPicard–Lindelöf theoremMathematical analysisDanskin's theoremBrouwer fixed-point theoremSqueeze theoremMathematicsCarlson's theoremMean value theorem
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A theorem of insertion and extension of functions for normal spaces

1993

Discrete mathematicsPure mathematicsArzelà–Ascoli theoremIsomorphism extension theoremFréchet spaceGeneral MathematicsClosed graph theoremRiesz–Thorin theoremOpen mapping theorem (functional analysis)Brouwer fixed-point theoremMathematicsCarlson's theoremArchiv der Mathematik
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