The Lindemann–Weierstrass Theorem

2014 ◽  
pp. 15-18
Author(s):  
M. Ram Murty ◽  
Purusottam Rath
Keyword(s):  
Weierstrass Theorem

An Alternative Proof of the Lindemann-Weierstrass Theorem

2000 ◽  
pp. 649-653
Author(s):  
F. Beukers ◽  
J. P. Bézivin ◽  
P. Robba
Keyword(s):  
Alternative Proof ◽  
Weierstrass Theorem

Separation and Approximation in Topological Vector Lattices

1959 ◽  
Vol 11 ◽  
pp. 286-296 ◽  
Author(s):  
Solomon Leader
Keyword(s):  
Spectral Theory ◽  
Vector Lattice ◽  
Weierstrass Theorem ◽  
Fundamental Lemma ◽  
Vector Lattices ◽  
Integrable Functions ◽  
Nikodym Theorem

Spectral theory in its lattice-theoretic setting proves abstractly that the indicators of measurable sets generate the space L of Lebesgue-integrable functions on an interval. We are concerned here with abstractions suggested by the fact that indicators of intervals suffice to generate L. Our results show that the approximation of arbitrary elements of a topological vector lattice rests upon the ability to separate disjoint elements/ and g by an operation that behaves in the limit like a projection annihilating/ and leaving g invariant.The introduction of this concept of separation together with the notion of limit unit leads (via the Fundamental Lemma) to abstract generalizations of the Radon-Nikodym Theorem (Theorem 1) and the Stone-Weierstrass Theorem (Theorem 3).

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