∫_Ω X dP — the Lebesgue integral of a random variable against its probability measure. Linear functional and workhorse of probability.
Expectation E[X]
Related concepts
- Random variable
- Probability measure P
- Law of large numbers
- Central limit theorem
- Real numbers (ℝ)
- Lebesgue integral
- Moment generating function
- Characteristic function
- Jensen's inequality (probability)
- Markov's inequality
- Chebyshev's inequality (probability)
- Lebesgue constant for interpolation
- Shannon source coding theorem
- Shannon channel coding theorem
- Rate-distortion theory
- Typical set + AEP
- Kullback-Leibler divergence + relative entropy
- Mutual information
- Information bottleneck (Tishby)
- Kolmogorov-Loveland randomness