It is helpful to define the fluxsurface average operator:

(2.148) 
According to Equations (2.129) and (2.130),

(2.149) 
where is a general axisymmetric scalar field. Moreover,
.
Making use of Equations (2.121)–(2.123) and (2.129), it is easily demonstrated that

(2.150) 
where is a general axisymmetric (i.e.,
) vector field, and

(2.151) 
is the volume contained within the magnetic fluxsurface whose label is .