On Measure Invariance for a 2-valued Transformation
We consider a family S=S(a) of 2-valued transformations of special form on the segment [0,1] with measure $μ=\int p(x) dλ$, which is absolutely continuous with respect to the Lebesgue measure $λ$. We endow S with a set of weight functions $α=\{α_1(x),α_2(x)\}$ and find a criterion of measure invariance under the transformation. This criterion relates the three parameters $a$, $p$, $α$ to each other.
math.DS↗