ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4502 on D1158: Measure space
Difference of almost everywhere equal euclidean complex functions is almost everywhere zero
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $f, g : X \to \mathbb{C}^D$ are each a D5608: Euclidean complex function on $M$
(ii) \begin{equation} f \overset{a.e.}{=} g \end{equation}
Then \begin{equation} f - g \overset{a.e.}{=} 0 \in \mathbb{C}^D \end{equation}