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Author:   Claude Tricot ,  M. Mendes France
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1995 ed.
Dimensions:   Width: 15.60cm , Height: 2.00cm , Length: 23.40cm
Weight:   1.440kg
ISBN:  

9780387940953

ISBN 10:   0387940952
Pages:   324
Publication Date:   18 November 1994
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I. Sets of Null Measure on the Line.- 1. Perfect Sets and Their Measure.- 2. Covers and Dimension.- 3. Contiguous Intervals and Dimension.- II. Rectifiable Curves.- 4. What Is a Curve?.- 5. Polygonal Curves and Length.- 6. Parameterized Curves, Support of a Measure.- 7. Local Geometry of Rectifiable Curves.- 8. Length, by Intersections with Straight Lines.- 9. The Length by the Area of Centered Balls.- III. Nonrectifiable Curves.- 10. Curves of Infinite Length.- 11. Fractal Curves.- 12. Graphs of Nondifferentiable Functions.- 13. Curves Constructed by Similarities.- 14. Deviation, and Expansive Curves.- 15. The Constant-Deviation Variable-Step Algorithm.- 16. Scanning a Curve with Straight Lines.- 17. Lateral Dimension of a Curve.- 18. Dimensional Homogeneity.- IV. Annexes, References and Index.- A. Upper Limit and Lower Limit.- A.1 Convergence.- A.2 Nonconvergent sequences.- A.3 Nonconvergent functions.- A.5 Some applications.- B. Two Covering Lemmas.- B.1 Vitali’s lemma.- B.2 Covers by homothetic convex sets.- C. Convex Sets in the Plane.- C.1 Convexity.- C.2 Size of a convex set.- C.3 Breadth of a convex set.- C.4 Area of a convex set.- C.5 Convex hull.- C.6 Perimeter of the convex hull.- C.7 Area of the convex hull of a curve.- References.

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