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[<32FE312F6B74D9E6D8053E5615C7C227> <32FE312F6B74D9E6D8053E5615C7C227>] >> startxref -351323 +352569 %%EOF diff --git a/Secondo anno/Elementi di probabilità e statistica/sections/3-probabilità-reale.tex b/Secondo anno/Elementi di probabilità e statistica/sections/3-probabilità-reale.tex index 2c89033..e6cac47 100644 --- a/Secondo anno/Elementi di probabilità e statistica/sections/3-probabilità-reale.tex +++ b/Secondo anno/Elementi di probabilità e statistica/sections/3-probabilità-reale.tex @@ -225,14 +225,16 @@ piccola di $\PP(\RR)$, la $\sigma$-algebra dei boreliani, che ci permette di esc L'affermazione (ii.) segue dal fatto che per ogni successione decrecente da destra $(x_i)_{i \in \NN} \goesdown \tilde{x}$ è - tale per cui $((-\infty, x_i])_{i \in \NN} \goesdown (-\infty, \tilde{x})$, e dunque + tale per cui $((-\infty, x_i])_{i \in \NN} \goesdown (-\infty, \tilde{x}]$, e dunque $(P(x_i))_{i \in \NN} \goesdown P(\tilde{x})$. \end{proposition} -% \begin{remark} -% La continuità a sinistra non è invece garantita dacché ogni successione da sinistra crescente $(x_i)_{i \in \NN} \goesup \tilde{x}$ -% è tale per cui -% \end{remark} +\begin{remark} + La continuità a sinistra non è invece garantita dacché non è vero che per ogni successione da sinistra crescente + $(x_i)_{i \in \NN} \goesup \tilde{x}$ + vale che $((-\infty, x_i])_{i \in \NN} \goesup (-\infty, \tilde{x}]$. Infatti, se $\tilde{x}$ non appartiene a tale + successione, l'insieme limite è $(-\infty, \tilde{x})$ e non $(-\infty, \tilde{x}]$. +\end{remark} \begin{proposition}[$P$ è univocamente determinata da $F$] Sia $F : \RR \to \RR$ una funzione tale per cui: