Displaying similar documents to “α-Equivalence”

Measures and lacunary sets

Pascal Lefèvre (1999)

Studia Mathematica

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We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.

One-parameter subgroups and the B-C-H formula

Wojciech Wojtyński (1994)

Studia Mathematica

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An algebraic scheme for Lie theory of topological groups with "large" families of one-parameter subgroups is proposed. Such groups are quotients of "𝔼ℝ-groups", i.e. topological groups equipped additionally with the continuous exterior binary operation of multiplication by real numbers, and generated by special ("exponential") elements. It is proved that under natural conditions on the topology of an 𝔼ℝ-group its group multiplication is described by the B-C-H formula in terms of the...

On the size of approximately convex sets in normed spaces

S. Dilworth, Ralph Howard, James Roberts (2000)

Studia Mathematica

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Let X be a normed space. A set A ⊆ X is approximately convexif d(ta+(1-t)b,A)≤1 for all a,b ∈ A and t ∈ [0,1]. We prove that every n-dimensional normed space contains approximately convex sets A with ℋ ( A , C o ( A ) ) ≥ l o g 2 n - 1 and d i a m ( A ) ≤ C √ n ( l n n ) 2 , where ℋ denotes the Hausdorff distance. These estimates are reasonably sharp. For every D>0, we construct worst possible approximately convex sets in C[0,1] such that ℋ(A,Co(A))=(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.