On the approximate differentiability of inverse maps

2014 ◽  
Vol 15 (2) ◽  
pp. 473-499 ◽  
Author(s):  
Luigi D’Onofrio ◽  
Carlo Sbordone ◽  
Roberta Schiattarella
Keyword(s):  
Approximate Differentiability

N-Lusin property in metric measure spaces: A new sufficient condition

2018 ◽  
Vol 30 (6) ◽  
pp. 1475-1486
Author(s):  
Marcela Garriga ◽  
Pablo Ochoa
Keyword(s):  
Measure Zero ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Metric Measure Spaces ◽  
Type Estimate ◽  
Measure Spaces ◽  
Approximate Differentiability

Abstract In this work, we are concerned with the study of the N-Lusin property in metric measure spaces. A map satisfies that property if sets of measure zero are mapped to sets of measure zero. We prove a new sufficient condition for the N-Lusin property using a weak and pointwise Lipschitz-type estimate. Relations with approximate differentiability in metric measure spaces and other sufficient conditions for the N-Lusin property will be provided.

On continuous functions with graphs of σ-finite linear measure

1974 ◽  
Vol 76 (1) ◽  
pp. 33-43
Author(s):  
James Foran
Keyword(s):  
Bounded Variation ◽  
Finite Length ◽  
Continuous Functions ◽  
Linear Measure ◽  
Image Position ◽  
Approximate Differentiability ◽  
Finite Linear

In this paper comparisons are made between the class of continuous functions of generalized bounded variation and the class of continuous functions with graphs having σ-finite length i.e. linear measure. An investigationof the differentiability and approximate differentiability of such functions discloses the fact that the latter class is considerably more extensivethan the former one. The following definitions will be needed:(1) A function f is said to be of bounded variation (VB) on a set E ifwhere the supremum is taken over all sequences {[ai, bi]} of non-overlapping intervals with endpoints in E.

scholarly journals On the k-pseudo-symmetrical approximate differentiability

1981 ◽  
Vol 114 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Giuseppina Russo ◽  
Santi Valenti
Keyword(s):  
Approximate Differentiability
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