# Are sentences from the same document independent and identically distributed?

I am trying to build an LSTM model to generate Shakspeare-like poems. I have data set $$\{s_1, s_2, \dots, s_m \}$$, which are sentences of Shakespeare poems, and each sentence contains words $$\{w_1, w_2, \dots, w_n \}$$.

I am wondering: Are different $$s_i$$ ($$i=1, \dots, m$$) independent and identically distributed samples (IID)? Are $$w_i$$ ($$i=1, \dots, n$$) within each sentence the IID?

The sentences coming from the same document, author, etc., are unlikely to be independent, that is, the occurrence of a sentence $$s_i$$ in a certain document $$d$$ is likely correlated with the occurrence of another sentence $$s_j$$. If they are not independent, they can also not be independent and identically distributed (which is a stronger condition). The same can be said for words in the same sentence.