ThmDex – An index of mathematical definitions, results, and conjectures.
Result R3971 on D1158: Measure space
Intersection of sets of infinite measure need not have infinite measure
Formulation 0
Let $M = (\mathbb{R}, \mathcal{L}, \mu)$ be a D5268: Real lebesgue measure space such that
(i) \begin{equation} E : = (- \infty, 1] \end{equation}
(ii) \begin{equation} F : = [-1, \infty) \end{equation}
Then
(1) \begin{equation} E, F \in \mathcal{L} \end{equation}
(2) \begin{equation} \mu(E) = \infty = \mu(F) \end{equation}
(3) \begin{equation} \mu(E \cap F) = 2 \end{equation}