Analytic Functions - download pdf or read online

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By Stanislaw Saks

ISBN-10: 0444408738

ISBN-13: 9780444408730

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A (cf. § 1, p. 2). A set Z in the plane is said to be ·bounded if it does not con­ tain the point oo and if the set of absolute values of the points zeZ is bounded, i. e. if there exists a. real finite number m such that JzJ

Theory of sets. 20 diameter of a set we mean the upper bound of the distances between any two points of this set. If a is an arbitrary point of the plane and r an arbitrary non­ negative real number (finite 6r infinite), then we shall denote by K(a;r) - when a=ftoo satisfying the set - the set of all points z different from oo and inequality e(a,z)

Next, from the sequence {b� llk = i,2, , whose points belong to the set B<2>, we can extract 2 a subsequence lb�} lt=i,2, convergent in the space A< J. The ••• ••• ••• sequence 1 {(b� J, space b� l A. A. is therefore compact. We can regard the Cartesian m-th power r of the plane E as an example of a Cartesian product of spaces. ,z are call the • • • neighbourhood hood with centre (z ,z2). 1 and z(l)' points of the plane. ,z�m>) in the space Em we shall mean the lar­ k gest of the numbers e(z<�>,z� >) for k=l,2, ...

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Analytic Functions by Stanislaw Saks


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