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Description
Statistical Independence in Probability, Analysis and Number TheoryThis concise monograph in probability by Mark Kac, a well known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in various contexts cutting across different mathematical
This concise monograph in probability by Mark Kac, a well-known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in various contexts cutting across different mathematical disciplines."The treatment begins with an examination of a formula of Vieta that extends to the notion of statistical independence. Subsequent chapters explore laws of large numbers and mile Borel's concept of normal numbers; the normal law, as expressed by Abraham de Moivre and Andrey Markov's method; and number theoretic functions as well as the normal law in number theory. The final chapter ranges in scope from kinetic theory to continued fractions. All five chapters are enhanced by problems.
Binding Type: Paperback
Publisher: Dover Publications
Published: 08/15/2018
ISBN: 9780486821580
Pages: 112
Weight: 0.26lbs
Size: 8.00h x 5.00w x 0.30d
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★★★★★ 5
Small dog dream toy
Size: Small, Color: Assorted Color
Small dog dream toy
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Reviewed in the United States on March 7, 2026
★★★★★ 5
Perfect for Small to Medium Dogs
Size: Small, Color: Assorted Color
Little Louise loves these little toys! Couldn’t be more happy with this purchase. Highly recommend for small to medium dogs!
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Reviewed in the United States on December 25, 2025
★★★★★ 5
Awesome ball and made to last!
Color: Black & Yellow
Awesome ball! My dog loves it and plays with it all the time. He's a very aggressive chewer and there are only a few toys he can have without destroying them. Very pleased with this.
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Reviewed in the United States on May 27, 2026
★★★★★ 5
Pretty tough
Color: Black & Lake Blue
I think the toy is great, but my dog was not excited about it. He prefers the original type which is larger. I think it could possibly be cracked open by a dog with a large mouth and is intent on getting the noise maker out. But it is pretty tough.
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Reviewed in the United States on April 22, 2026
★★★★★ 3
Bite proof
Color: Blue & Red
The ball is tough but it will not take the dog having it all the time .play with them and put it up or it will not last price not bad
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Reviewed in the United States on May 24, 2026