Adding to paragraph 1 Кнышев-статья.en pdf file. The main theorem. The interval is the sum of the final or a countable number of pairs not intersecting intervals. For the function definition interval, there is a sum intervals on each of which the function is invertible (strictly monotone). This is a non-degenerate function. For any sum of intervals, there is an interval of which function is not reversible. This is a degenerate function. The measure of the sum of the intervals is equal to the measure of the interval functions. For a nondegenerate function, each interval must be maximally continue on the basis of reversibility (strict monotony). That will give a single sum of intervals. Sole in meaning that no interval from the sum is continued by reversibility is impossible.
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