I have a problem that can be resolved if i show that $$E(\varepsilon_k\mid\sigma(\varepsilon_1,\ldots,\varepsilon_{k-1}))=E(\varepsilon_k)$$ where $\varepsilon_1,\ldots,\varepsilon_k$ $\sim \mathcal{N}(0,1)$ and i know they are independent.
I dont know where to even start. Any proof or help would be great.