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Published equation contexts

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]

Why this formula appears here

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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pϵp_{\epsilon}

Symbol p_epsilon

pep_epsilon is part of the quantity the equation computes from the expression on the right.

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GG

Symbol G

G appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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dd

Symbol d

d appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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gg

Symbol g

g appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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g^\hat g

Symbol hat g

hat g appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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ϵ\epsilon

Symbol epsilon

epsilon appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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GG

Starting index or lower bound: G

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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d(g^,g)≤ϵd(\hat g,g)\leq\epsilon

Starting index or lower bound: d(hat g,g) ≤ epsilon

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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].

Equation 42 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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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