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Equation 42 · Part 12 · A Reference Frame Becomes Classical by Publishing Its Orientation

subscript

pϵ(F)=∫Gdg∫d(g^,g)≤ϵTr⁡ ⁣[ρF(g)MF(dg^)].p_{\epsilon}(F)= \int_G dg\int_{d(\hat g,g)\leq\epsilon} \operatorname{Tr}\!\left[\rho_F(g)M_F(d\hat g)\right].
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

For a Haar-uniform prior, define the fragment success probability pϵ(F)=∫Gdg∫d(g^,g)≤ϵTr⁡ ⁣[ρF(g)MF(dg^)]p_{\epsilon}(F)= \int_G dg\int_{d(\hat g,g)\leq\epsilon} \operatorname{Tr}\!\left[\rho_F(g)M_F(d\hat g)\right]. This is again a definition. The Haar measure dg is normalized to one. A frequentist worst-case version could replace the average over g with an infimum; the two must not be mixed after seeing results.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.