What is the difference between a transition function and a transition kernel?

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Context of Question:

"Algorithms for Reinforcement Learning", Csaba Szepesvari pg 11

Excerpt:

In the case of the inventory control problem, the MDP was conveniently specied by a transition function f (cf., (4)). In fact, transition functions are as powerful as transition kernels: any MDP gives rise to some transition function f and any transition function f gives rise to some MDP.