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In the mathematical discipline of measure theory, a Banach measure is a certain way to assign a size to all subsets of the Euclidean plane, consistent with but extending the commonly used Lebesgue measure. While there are certain subsets of the plane which are not Lebesgue measurable, all subsets of the plane have a Banach measure. On the other hand, the Lebesgue measure is countably additive while a Banach measure is only finitely additive.
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