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Symmetric derived number

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at a point

A generalization of the ordinary notion of a derived number (cf. Dini derivative) to the case of a set function on an -dimensional Euclidean space. The symmetric derived numbers of at are defined as the limits

where is some sequence of closed balls with centres at and radii such that as .

The -th symmetric derived numbers at of a function of a real variable are defined as the limits

where as and is the symmetric difference of order of at .

References

[1] S. Saks, "Theory of the integral" , Hafner (1937) (Translated from French)


Comments

References

[a1] W. Rudin, "Real and complex analysis" , McGraw-Hill (1974) pp. 24
How to Cite This Entry:
Symmetric derived number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Symmetric_derived_number&oldid=48923
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article