Mathematical Methods for Elastic Plates by Christian Constanda

Author:Christian Constanda
Language: eng
Format: epub
Publisher: Springer London, London

(4.25)

where and are the limits almost everywhere of increasing sequences of step functions and , respectively, for which the corresponding sequences of integrals and are bounded.

4.11 Definition. Let A point such that

where the are as in (4.25), is called a Lebesgue point for .

4.12 Lemma. If and is a Lebesgue point for , then

The proof of this assertion is based on (4.25) and Definition 4.11.

4.13 Theorem. Let be a proper -singular kernel in , , let

and suppose that

(4.26)

and

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