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Posplošitve izreka o monotoni konvergenci
Lavrič, Boris
Izrek o monotoni konvergenci realnih zaporedij razširimo na končnorazsežne delno urejene vektorske prostore. Dokažemo, da sta v končno razsežnem arhimedskem delno urejenem vektorskem prostoru ▫$V$▫ ...za nenegativna realna števila ▫$\alpha_1,...,\alpha_p$▫ ekvivalentni naslednji izjavi: (i) Vsako omejeno zaporedje ▫$(x_n)_{n=1}^\infty$▫ prostora ▫$V$▫, ki ustreza pogojem ▫$$x_{n+p} \ge \sum_{j=1}^p \alpha_jx_{n+p-j}, \quadd n=1.2.....$$▫ je konvergentno; (ii) Velja ▫$\sum_{j=1}^p \alpha_j = 1$▫, poleg tega pa so naravna števila ▫$j \le p$▫, ki ustrezajo pogoju ▫$\alpha_j > 0$▫, tuja.
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