Theorem: Sufficient condition for tightness (Bounded in probability)

Theorem: Sufficient condition for tightness: Prove: If there’s a function 𝜙(𝑥)≥0 for all 𝑥 such that 𝜙(𝑥)→∞ as |𝑥|→∞ and: 𝐶=sup𝑛∫𝜙(𝑥)𝑑𝐹𝑛(𝑥) is finite, then {𝐹𝑛} is tight.