 An important feature of \(X\) is that it is endowed with a so-called measure \(\mu\). We are familiar with measures in many contexts: from a mathematical point of view, the length that we attribute to a part of a line, the surface we attribute to a part of a plane, and the volume we attribute to a segment of space are measures. A measure is simply a device to attribute a ‘size’ to a part of a space. Although \(X\) is an abstract mathematical space, the leading idea of a measure remains the same: it is a tool to quantify the size of a set. So we say that the set \(A\) has measure \(\mu(A)\) in much the same way as we say that a certain collection of points of ordinary space (for instance the ones that lie on the inside of a bottle) have a certain volume (for instance one litre).