1.1. Two complex measurable functions/ and g on complex measure spaces (X, η) and (Y, v) are equimeasurable, abbreviated ƒ ∼ g, if
for every Borel set E ⊆ C. If Φ is a continuous complex function on C, then we make the following standing hypothesis (HI) which relates Φ, f, and g:
(HI) For all α, β ∊ C, we have