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Probability Theory by Raphael Tavares de Alencar, Marcelo Sampaio de Alencar

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         CHAPTER 7         

CONVERGENCE AND THE LAW OF LARGE NUMBERS

Convergence is the law.

7.1  FORMS OF CONVERGENCE IN PROBABILITY THEORY

The Mathematics of the nineteenth century was very creative. However, in some areas, such as Integral Calculus, it lacked the necessary rigor. Number theory is another example, especially regarding the convergence limits of sequences. Karl Weierstrass (1815–1897), a high school teacher in a small German town, was responsible for introducing exactitude in the analytical arguments of the time and, despite his proverbial lack of interest in publishing his results, he became known as the father of modern analysis (Dunham, 2005).

Weierstrass was the first to recognize the dichotomy between pointwise convergence ...

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