Usual hypotheses

In probability theory, given a probability space $(\Omega,\mathcal{F},\mathbb{P})$, a filtration $\mathbb{F} = \{ \mathcal{F}_{t} \}_{t \geq 0}$ is said to satisfy the usual hypotheses if:^[1]

1. $\mathcal{F}_{0}$ contains all $\mathbb{P}$-negligible events.
2. $\mathbb{F}$ is right-continuous.

References

1. Pascucci, Andrea. Pde and Martingale Methods in Option Pricing. Berlin: Springer, 2011.