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Based on Conjecture 4.7, we will consider only functions g that are monotonically increasing on each interval.
(ZL FE sibling point relation): Let g be monotonously increasing on each interval A s, with (g(A_{0})=cdots =g(A_{N-1})=mathcal {W}).
Thus A is strictly increasing on each of (L_{3}) and (L_{4}) when we move from O to points where A takes the value b.
(ZL is equivalent to quantile relationship between sibling points): Let g be monotonously increasing on each interval A s, with (g(A_{0})=cdots =g(A_{N-1})=mathcal {W}).
In Section 4.1, we present a chain of arguments from which we conclude that, for ZL helper data, it is sufficient to consider only functions g with the following properties: (1) covering (mathcal {W}) on each quantization interval (surjective); (2) monotonically increasing on each quantization interval.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com