Contrapunctus of the continuum problem and the measure problem

In the long history of CH (Continuum Hypothesis) and its exten- sions into CP (Continuum Problem) that determines cardinalities of all power sets, solutions of the later are related in a variety of ways with the solution of the measure problem. = ℵF(α), which is referred as The Continuum Problem. This equation, after Cantor diagonal theorem can be written as (∀α ∈ ORD)2 ℵ α = ℵα+f(α), where f (α) 1 for all ordinals α. When f = 1 the last equation becomes a formulation of the Generalized Continuum Hypothesis - GCH. The function f here we call CP displacement function. The major excitement about solution of CP