The paper by G. Mathéron introduces the concept of intrinsic random functions (IRF), which are a generalization of stationary random functions. IRF are used to model non-stationary phenomena and have broader statistical inference capabilities. The key topics covered include: 1. **Definition and General Properties**: IRF are defined as linear mappings from a subspace of measures to a Hilbert space, with properties such as translation invariance and the existence of a generalized covariance (GC). 2. **Generalized Covariances (GC)**: GC for IRF are conditionally positive definite functions, and their existence and uniqueness are established. The paper provides examples of GC and discusses their applications in statistical inference. 3. **Best Linear Intrinsic Estimators (BLIE)**: BLIE are used for estimating functionals of IRF, such as values at specific points or integrals. The paper provides conditions for the existence and uniqueness of BLIE, including finite and infinite cases. 4. **Turning Bands Method**: This method is used for simulating IRF, providing a practical approach to generating random functions with specific properties. 5. **Polynomial GC**: Models with polynomial GC are discussed, as they allow for automatic statistical inference due to their linear dependence on unknown parameters. 6. **Locally Stationary k-IRF**: The concept of locally stationary IRF is introduced, where the function can be approximated by a stationary IRF up to a random polynomial, enabling the definition of a locally significant trend or drift. The paper aims to provide a theoretical foundation for automatic contouring procedures, particularly in the context of universal kriging, by exploring the properties and applications of IRF.The paper by G. Mathéron introduces the concept of intrinsic random functions (IRF), which are a generalization of stationary random functions. IRF are used to model non-stationary phenomena and have broader statistical inference capabilities. The key topics covered include: 1. **Definition and General Properties**: IRF are defined as linear mappings from a subspace of measures to a Hilbert space, with properties such as translation invariance and the existence of a generalized covariance (GC). 2. **Generalized Covariances (GC)**: GC for IRF are conditionally positive definite functions, and their existence and uniqueness are established. The paper provides examples of GC and discusses their applications in statistical inference. 3. **Best Linear Intrinsic Estimators (BLIE)**: BLIE are used for estimating functionals of IRF, such as values at specific points or integrals. The paper provides conditions for the existence and uniqueness of BLIE, including finite and infinite cases. 4. **Turning Bands Method**: This method is used for simulating IRF, providing a practical approach to generating random functions with specific properties. 5. **Polynomial GC**: Models with polynomial GC are discussed, as they allow for automatic statistical inference due to their linear dependence on unknown parameters. 6. **Locally Stationary k-IRF**: The concept of locally stationary IRF is introduced, where the function can be approximated by a stationary IRF up to a random polynomial, enabling the definition of a locally significant trend or drift. The paper aims to provide a theoretical foundation for automatic contouring procedures, particularly in the context of universal kriging, by exploring the properties and applications of IRF.