is_measurable

std.stats.is_measurable · Level L3

Whether a map f between finite measurable spaces (X, Σ_X) and (Y, Σ_Y), each σ-algebra listed in full, is measurable, as 1 or 0: the preimage f⁻¹(B) of every B ∈ Σ_Y is in Σ_X. The same preimage test as continuity; measurability implies neither continuity nor integrability.

B ∈ Σ_Y ⇒ f⁻¹(B) ∈ Σ_X

Signature

is_measurable(SX: f64[m, n], SY: f64[p, k], f: i64[n]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference every preimage among the members of Σ_X in exact rational arithmetic, on all 40 test cases.
All 40 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

is_continuous

Called by

—

sha256:6c46c86569df49841c698c85907a47a1e612c55d0e9b818529f2a5c6c49b23a4

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.is_measurable · Ω:is_measurable
Pins: sha256:7a1161c860cc7e2ef8e34d3f3792b646be391ae033fb98f8b1a1e85846fc4115this graph and the 1 it reaches through calls
Evidence: sha256:955fb9ebb32ccc3f51916feae9579193ffc24f534fc7df37ccf640410aecce6dthe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.