# miscellaneous

After years' study in probability, I felt more and more happy with the construction of probability space, it's so simple seemingly but interesting that may be applied to many more areas rather than math.

Let’s review a little bit about the probability space in math. Given a space $(\Omega, \mathbb{F}, \mathbb{P})$, assume that there exists a r.v $X s.t. \{\omega|X(\omega)>0\}\in\mathbb{F}$, then we can measure the events $\{X>0\}$ by using $\mathbb{P}(X>0)$. What’s more, adding a time dimension to make it a stochastic process $X_t(\omega)$, then we have properties like $\mathbb{F}_t\subset\mathbb{F}_{t^+}$ and so on.

Secondly, let’s consider another fact, different people have different decisions when given tasks, why is that? That apparently depends on the knowledge we own, how do I relate this decision making base on probability space construction idea? This attracts me these days and I’ll post what I think later.

To be continued……