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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
Yummie
Flavor Name: Rabbit, Size: 4 Ounce (Pack of 3)
My angel LOVES these treats!! Great product.
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Reviewed in the United States on May 2, 2026
★★★★★ 4
Small quick treat
Flavor Name: Rabbit, Size: 4 Ounce (Pack of 1)
Great treats. My boys loved them. They do vary in size and quite a few crumbs were left over in the bottom of the bag. No smell and they are not chewy, but cruchy because of the freeze dried process so I know they will hold up over time. Some pieces were thick but not hard. Being that these are freeze dried treats, the longevity should be great!
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Reviewed in the United States on March 24, 2026
★★★★★ 5
Absolutely The Best!!
Flavor Name: Rabbit, Size: 4 Ounce (Pack of 1)
Our dog (Aussie/Border Collie) has a sensitive stomach and these work great for her! She loves all the flavors (especially salmon and turkey & veggies) and at only about a calorie each, it's pretty much impossible for her to over eat. These work GREAT for training treats, too!
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Reviewed in the United States on March 25, 2026
★★★★★ 5
Pupford Freeze Dried Training Treats for Dogs & Puppies, 1400+ Two Ingredient Bites
Flavor Name: Rabbit, Size: 4 Ounce (Pack of 3)
My Australian Shepherd loves these treats and they're the perfect size for training.
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Reviewed in the United States on March 21, 2026
★★★★★ 5
Awesome quality balls -- my dog loves them!
Color: F) 3-Pack (2.5" Balls)
Love this 3 ball set and variety and quality. These are the 2.5" size, similar to a tennis ball size give or take. The fun citron yellow one is the thickest + heaviest, very bouncy, and tough. The blue is still tough but not as thick or bouncy, a bit more flexible. And the clearish one is the lightest/flexible and is glow in the dark [although we haven't tried that part yet]. I have a 7month old 40lb girl who is becoming like a power chewer on some things -- but hasn't done that with these. She can play, mouth them, chew them, not even one knick or anything. Yes! The citron and blue one we leave out all the time in her little toy box. They have holes in the middle and have used them to hold thinner bully sticks and other treats. The blue one is fun to put smaller treats inside that she can work out like a puzzle. Obviously they are fun for fetch! We leave the other up and only get out when we can play with her because label said it is not a chew toy so we didn't want to take chances. Overall super fun and cool and good quality, human and dog approved LoL. ***We ordered the 2 set of 4" balls, blue and purple [they are same consistency of the blue ball] and love these too! Very fun and good at using with treats the sticks too, plus these don't get lost under sofas and furniture like the smaller ones, a big plus.
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Reviewed in the United States on November 28, 2025
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