Colloquium publications.

AUTHOR'S PREFACE.

Most mathematicians are familiar with that development of
the subject of integral equations which is epitomized by the
name Hilbert. There are however other domains whose description is not so completely available in book form, which represent
nevertheless an expansion of the same circle of fundamental
notions, implied in the central theory of integral equations.
Volterra's genial concepts, developed during the last thirty years,
and outlined in his treatise of 1913, have by contact with the
ideas of Hadamard, Stieltjes, Lebesgue, Borel and others, given
rise to many new points of view. It is the purpose of the
Lectures to select for discussion some of those which appear most
to promise further rapid expansion.
A word may be necessary as to the arrangement. In order to
make the subject matter accessible to as large a circle of readers
as possible, the text in large type has been devised to be intelligible to those who approach the subject for the first time, and
may be read by itself. The text in small type comes, on the
other hand, closer to the present state of the subject, and may
be more suggestive. The author thus hopes to fulfil the avowed
purpose of the Colloquium.
Commas in formulhe are omitted when not necessary for clearness; thus r(X, t) is written r(Xt) if the meaning is clear from the
context.
The author has given references to American mathematicians
freely, in order that familiarity with names may stimulate conversation at meetings of the Society, and thereby increase interest
in the subject itself.
HOUSTON, TEXAS,
February, 1918.

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