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Every submartingale S of class D has a unique Doob-Meyer decomposition S = M + A, where M is a martingale and A is a predictable increasing process starting at 0.
A simpler proof of the Boros--Füredi--Bárány--Pach--Gromov theorem
simpler proof Boros--Füredi--Bárány--Pach--Gromov theorem
2011/3/1
A short and almost elementary proof of the Boros–F¨uredi–B´ar´any–Pach–Gromov theorem on the multiplicity of covering by simplices in Rd is given.
About the proof of the Fredholm Alternative theorems
the Fredholm Alternative theorems math
2010/11/23
In this short paper we review and extract some features of the Fredholm Alternative problem .
A Consistency Proof for Some Restrictions of Tait's Reflection Principles
Consistency Proof Restrictions Tait's Reflection Principles
2010/12/9
In [4] Tait identifies a set of reflection principles which he calls (2)n -reflection
principles which Peter Koellner has shown to be consistent relative to an Erd¨os cardinal
(!) in [1].
A Simple Proof of Thue's Theorem on Circle Packing
Simple Proof Thue's Theorem Circle Packing
2010/12/10
Thue's theorem states that the regular hexagonal packing is the densest circle packing in the plane. The density of this circle con guration is p12 0:906 90: