We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures over finite sequences, infinite sequences, and $T_0$, second countable topologies. One example is the convolution of signals over real numbers with probability kernels. Thus the smoothing of any signal due We show that given a quantum measurement, for an overwhelming majority of pure states, no meaningful information is produced.

翻译：我们将算法守恒不等式扩展到概率测度。概率测度的自信息量在经随机化处理后不会增加。这包括（可能不可计算的）有限序列、无限序列以及$T_0$、第二可数拓扑上的测度。一个例子是实数信号与概率核的卷积。因此，任何信号的平滑化均源于……我们证明，给定一次量子测量，对于绝大多数纯态，不会产生有意义的信息。