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THE theory of functions of a real variable is a subject of fairly recent date and is necessarily expanding as new theorems are discovered and fresh generalisations effected. On the other hand, the refinements of modern investigations make an ever-increasing demand for rigorous examination of their mathematical groundwork. For this reason the mathematical physicist cannot afford to remain ignorant of the progress of function theory. Prof. Hobson has an admirable gift of lucid exposition of the subject of which he is a master, and the reader can follow him with delight into realms which may occasionally appear to belong to philosophy rather than to mathematics.
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Hobson et al. (1958) studied this question.
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