Remark. Finite and measurable probability laws [ftip-000C]
Remark. Finite and measurable probability laws [ftip-000C]
A finite vocabulary and a bounded token sequence admit probability laws expressed as ordinary sums, with explicit normalization and conditioning. The finite-sequence interface matches [phuong2022formal, sec. 3, Sequence modelling].
States, observations, and tool outputs need not be finite. In that setting \(\Delta (X)\) is replaced by probability measures on a declared measurable space and conditional laws are probability kernels. Results on finite spaces need additional measurable-space hypotheses before they apply in this setting.