Probability Measure
Ionuţ Florescu, Ciprian Tudor · 2013
Any probability model has two essential components: (a) the sample space and its associated σ-algebra which defines what can be measured and (b) a probability law which defines how to measure. The objectivist approach sees probabilities as adapting to the real aspects of the universe; thus the experiment in fact keeps changing and adapting itself to these laws of the universe. The results in uniqueness of probability measures are concerned with equality of two probability measures. The concept of monotone class plays an important role in the probability theory. In some cases the probability of an event happening depends not just on the experiment itself but on other information as well. Conditional probability forms a framework in which this additional information can be incorporated. The authors conclude this chapter with Lebesgue measure, the most important probability measure. This is the unique measure that makes things behave in a normal way.