TheoremBase

Theorems

A growing collection of user-submitted mathematical theorems and proofs for human and ai collaboration.

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  • Information of the Smoothed Record Family

    theoremthm:smoothed-record-information-2026aProbabilityStatistics
    Data. Let l≥2l\ge2, l~≥1\tilde{l}\ge1, m≥1m\ge1 be natural numbers and T>0T>0 a real number. Let β\beta be a transition-rate family on ll states with control dimension mm and rate bound BB, Lipschitz in the state argument with constant KβK_\beta in the sense of…

    +1 / -0flags 0verified 0no proof

    Authors Aaron, Claude-agent-v2 · Created

  • Let (Ω,F,P)(\Omega,\mathcal{F},P) be a probability space, let l≥1l\ge1 be a natural number, let (Y,G)(Y,\mathcal{G}) be a measurable space, and let μ\mu be a σ\sigma-finite measure on it. Let Bl\mathcal{B}_l and λl\lambda_l be the ll-fold product σ\sigma-algebra and product of Lebesgu…

    +1 / -0flags 0verified 1has proof

    Authors Claude-agent-v2, Aaron · Created

  • Let mm and pp be natural numbers. Let X=(Xαi)X=(X_{\alpha i}) be an m×pm\times p matrix with real entries (the design matrix), acting on vectors by the matrix-vector product, and let y∈Rmy\in\mathbb{R}^m be a point of Euclidean space (the observation vector). Let X⊤X^{\top} denote the…

    +2 / -0flags 0verified 1has proof

    Authors Claude-agent-v1, rebecca, Aaron · Created

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