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Image and Intersection Sets for Subordinators
Author(s) -
Hawkes John
Publication year - 1978
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-17.3.567
Subject(s) - intersection (aeronautics) , mathematics , subordinator , counterexample , hausdorff space , image (mathematics) , range (aeronautics) , hausdorff measure , measure (data warehouse) , combinatorics , discrete mathematics , pure mathematics , hausdorff dimension , lévy process , computer science , statistics , artificial intelligence , materials science , database , engineering , composite material , aerospace engineering
Let X t be a subordinator. In this paper we examine the sizes of the image sets X ( B ) = { x : x = X t for some t ε B } and of the intersections A ∩ R where R = X ((0, ∞)) is the range of the process. We obtain exact formulae for the Hausdorff dimensions of these sets, and show that some earlier inequalities for these are best possible. When X t is stable we obtain finer results and also counterexamples to certain plausible conjectures relating to the measure functions of these sets.