New answers tagged uniform-integrability
1
vote
Details on the proof of: Suppose $X_n \xrightarrow{\mathbb{P}} X$. $X_n$ is uniformly integrable (u.i.) $\implies$ $X_n \xrightarrow{L^1} X$
For (1), I think you want $\varepsilon/6$ instead of $\varepsilon/3$ in your equation (*). Then one has
\begin{align*}
\mathbb{E}[K1_{|X_n| > K}] + \mathbb{E}[|X_n| 1_{|X_n| > K}] &\le \...
- 11.5k
Top 50 recent answers are included