Let $(\Omega ,\mathcal F,\mathbb P)$ a probability space and $X_n=(X_n(t))_{t\in [0,T]}$ a stochastic process. Let $Y_n=(Y_n(t))_{t\in [0,T]}$ a random process. What does $$|Y_n(t)|\leq 1+|X_n(t)|,$$ for all $t$ and all $n$.
1) Does it mean $$\mathbb P(|Y_n(t)|\leq 1+|X_n(t)|)=1$$ for all $n$ and all $t$, or $$\mathbb P(\forall t,\forall n, |Y_n(t)|\leq 1+|X_n(t)|)=1\ \ ?$$