Analytical limit value concept

Analytical concept of limit value , also: limit value of the relative frequency, established by Richard von Mises in 1919.

The probability of an event : ${\displaystyle {\mathcal {A}}}$

${\displaystyle {\mathcal {P}}({\mathcal {A}})=\lim _{n\to \infty }{\mathcal {H}}({\mathcal {A}},n)=\lim _{n\to \infty }{n_{\mathcal {A}} \over n}}$

With

${\displaystyle {\mathcal {H}}({\mathcal {A}},n)}$ : relative frequency

${\displaystyle n_{\mathcal {A}}}$ : Number of favorable cases

${\displaystyle n}$ : Number of attempts

Example: Plotting the relative frequency in a cube trial of an event "The dice sum is 7" and the number of trials in a diagram, it must be observed that with increasing number of attempts against the probability sought. ${\displaystyle {\mathcal {H}}({\mathcal {A}},n)}$ ${\displaystyle n}$ ${\displaystyle {\mathcal {H}}({\mathcal {A}},n)}$ ${\displaystyle n/}$ ${\displaystyle {\mathcal {P}}({\mathcal {A}},n)}$

An axiomatization of the probability theory was only achieved in 1933 by Kolmogorow . See also: Axiomatization of probability theory