Learning.Environment.obs0
From the authors
Distribution of the first observation: the observation kernel at time 0 applied to the empty
history.
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๐ : Type u_1m๐ : MeasurableSpace ๐A measurable space is a space equipped with a ฯ-algebra. -
๐ : Type u_2m๐ : MeasurableSpace ๐ -
๐จ : Type u_3m๐จ : MeasurableSpace ๐จ
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env : Environment ๐ ๐ ๐จA stochastic environment.
MeasureTheory.Measure ๐(env.obs 0) defaultMeasurableSpace : Type u_6 โ Type u_6A measurable space is a space equipped with a ฯ-algebra.
Learning.Environment : (๐ : Type u_5) โ
(๐ : Type u_6) โ
(๐จ : Type u_7) โ [MeasurableSpace ๐] โ [MeasurableSpace ๐] โ [MeasurableSpace ๐จ] โ Type (max (max u_5 u_6) u_7)A stochastic environment. At each round, an observation is drawn prior to the algorithm taking an action. Then the environment provides feedback based on the observation and the action.Go to its page
MeasureTheory.Measure : (ฮฑ : Type u_5) โ [MeasurableSpace ฮฑ] โ Type u_5A measure is defined to be an outer measure that is countably additive on measurable sets, with the additional assumption that the outer measure is the canonical extension of the restricted measure. The measure of a set `s`, denoted `ฮผ s`, is an extended nonnegative real. The real-valued version is written `ฮผ.real s`.
Inhabited.default : {ฮฑ : Sort u} โ [self : Inhabited ฮฑ] โ ฮฑ`default` is a function that produces a "default" element of any `Inhabited` type. This element does not have any particular specified properties, but it is often an all-zeroes value.
Code
def Environment.obs0 (env : Environment ๐ ๐ ๐จ) : Measure ๐ := env.obs 0 default deriving IsProbabilityMeasure
Meaning last changed in v4.34.0-rc2-76-g565f652 (2026-09-10).
Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file ยท open it in the Lean web editor.
Dependency graph
Audit surface: 3 project declarations, 16 external constants
โ Proved: no sorry anywhere in its closure
This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.