This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...rectangles enclosing all the points of the arc have in common has a lower limit greater than zero. The two continuous functions f(t), 4 (t), which define x, y as functions of ty possess for no value of t definite differential coefficients, and are perhaps the simplest examples of continuous non-differentiable functions ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...rectangles enclosing all the points of the arc have in common has a lower limit greater than zero. The two continuous functions f(t), 4 (t), which define x, y as functions of ty possess for no value of t definite differential coefficients, and are perhaps the simplest examples of continuous non-differentiable functions. 248. It might at first sight appear that a curve having the same properties as that of Peano might have been defined by restricting t--'axa... to be such that an infinite number of digits other than 0 are present, and then defining x, y by x = 'axaab..., y='a2a4a6.... If however the double representation of x, y were not restricted, as in the case of t, there would be no value of t corresponding to, say, #=1000..., 2/ =-2000.... If (x, y) were on the other hand so restricted, there would be no values of (xy y) corresponding, for example, to $ = 111010101.... It thus appears that some such rule as that given by Peano is necessary to obviate the difficulty caused by the double representation of a certain class of rational numbers, in a given scale. The method may easily be extended to obtain a continuous correspondence between the points in a cube and those in a linear interval. A somewhat different method of establishing correspondence between the points of the square, and those of the linear interval, is the following: ---Let tx denote one of the perfect set of points defined by Qj Qj2 Ct3 when every a is either 0 or 2. For such a point tu oo and y may be denned by I/O;.o., a., 2V2 22 + 23+ A point t which does not belong to the perfect set is interior to one of the See Lebesgue, Legons sur Vintegration, p. 44. complementary intervals ( /, /') of the set; in such an interval we may define #, 2/ as linear functions of t, thus where ...
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Add this copy of The Theory of Functions of a Real Variable and the to cart. $23.11, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 1957 by Dover Publications.
Edition:
1957, Dover Publications
Details:
Publisher:
Dover Publications
Published:
1957
Alibris ID:
18254479826
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Third edition; 2 vols., 726 + 778 pp., paperbacks, light wear to spines and covers else text clean & bindings tight. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
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Very Good. Very Good condition. Slipcase Acceptable. 2 Volume Set. (Mathematics) A copy that may have a few cosmetic defects. May also contain light spine creasing or a few markings such as an owner's name, short gifter's inscription or light stamp. Bundled media such as CDs, DVDs, floppy disks or access codes may not be included. NOT AVAILABLE FOR SHIPMENT OUTSIDE OF THE UNITED STATES.
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Volume 2. This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In fair condition, suitable as a study copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 1600grams, ISBN:
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Volume 1. This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In good all round condition. Re-bound by library. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 1350grams, ISBN:
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
