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Fundamental Theorems of Calculus for Packing Measures on the Real Line
Author(s) -
Haase H.
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211480119
Subject(s) - mathematics , envelope (radar) , bounded function , hausdorff space , real line , almost everywhere , bounded variation , calculus (dental) , derivative (finance) , line (geometry) , interval (graph theory) , pure mathematics , discrete mathematics , mathematical analysis , combinatorics , geometry , medicine , telecommunications , radar , dentistry , computer science , financial economics , economics
The fundamental Theorems of Calculus are extended to the treatment of packing measures on the real line. These are related to the corresponding result for Hausdorff measures. We prove that the centered inner‐envelope derivative and the outer‐envelope derivative of a continuous increasing function on an interval differ, but in a certain sense they are almost everywhere linear and the theorems are true for h ‐continuous almost h ‐singular functions of bounded variation.